Download LABORATORY MANUAL (Modern Physics & General Optics) PL – 402 (2013-2014)

LABORATORY MANUAL
(Modern Physics & General Optics)
PL – 402 (2013-2014)
School of Physical sciences
NATIONAL INSTRITUTE OF SCIENCE EDUCATION AND RESEARCH (NISER)
BHUBANESWAR
Last updated December 2013, NISER, Bhubaneswar
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LIST OF EXPERIMENTS (PL – 402)
1. Determination of Planck’s constant and work function of metals using Photoelectric effect
2. Franck-Hertz Experiment with Hg-tube: Inelastic scattering of electrons by atoms
3. Study of Hydrogen Spectra (Balmer Series) and determination of Rydberg’s constant
4. Study of emission spectra of metals using constant deviation spectrometer
5. Interference of light using Fresnel’s Bi-prism and Mirror
6. Study of different fringe patterns using Michelson’s Interferometer
7. Alignment of Fabry- perot Interferometer and study of the fringe patterns
8. Determination of wavelength of laser using Michelson’s interferometer
9. Study of sodium D-lines using a grating spectrometer
10. The velocity of Ultrasonic waves in liquid by the Debye-seares Effect
11. Study of polarization by verification of Malus’ Law
Appendix: Support manual for prism spectrometer
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EXPT# 01: Determination of Planck’s constant and work
function of metals using photoelectric effect
Introduction
One of the most important experiments from the early 20th century was the photoelectric effect
experiment. In this experiment, shinning a light upon a metal surface may cause electrons to be
emitted from the metal. In 1905, Albert Einstein working in a Swiss patent office published a
paper in which he explained the photoelectric effect. He argued that light was not a wave – it is
particulate – and it travels in little energy bundles (or packets) called photons. The energy of one
of these photons is hν, where h is the fundamental constant of nature recently proposed by Max
Planck to explain blackbody radiation, and ν is the frequency of the photon. This novel
interpretation of light turned out to be very significant and secured a Nobel Prize for Albert
Einstein. Robert Millikan, co-founder of the California Institute of Technology and fellow Nobel
Prize Winner, performed the careful experimental verification of Einstein’s predictions.
Objective:

To determine Planck’s constant ‘h’ from the stopping voltages measured at different
frequencies (wavelengths) of light.

To determine the work function “” of metal sample.
Apparatus:

Photocell

High intensity Hg
lamp

Grating

Electrometer amplifier

Digital multimeter

Colour filters (525 and
580 nm).
Theoretical Background:
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An electron in a metal can be modeled as a being in an average potential well due to the net
attraction and repulsion of protons and electrons. The minimum depth that an electron is located in
the potential well is called the work function of the metal,  (see Fig. 1). In other words, it is a
measure of the amount of work that must be done on the electrons (located in the well) to free it
from the metal. Since different metal atoms have different number of protons, it is reasonable to
assume that the work function () depends on the metal. This is also supported by the fact that
different metals have different values for electrical properties that should depend on the electron
binding including conductivity. The electron in the potential well of a metal is shown below in Fig.
1. It is analogous to a marble trapped in a water-well. The shallower the well (i.e. the lower the
work function “”) then the less energy required to cause the emission of the electron. If we shine
a light with sufficient energy then an electron is emitted.
E=0
E = -e 
Fig. 1 Electron in a potential well at a depth “”
When a photon with frequency “ν” strikes the surface of a metal, it imparts all of its energy
to a conduction electron near the surface of the metal. If the energy of the photon (hν) is greater
than the work function (), the electron may be ejected from the metal. If the energy is less than
the work function, the electron will simply acquire some kinetic energy that will dissipate almost
immediately in subsequent collisions with other particles in the metal. By conservation of energy,
the maximum kinetic energy with which the electron could be emitted from the metal surface Tmax,
is related to the energy of the absorbed photon hν, and the work function , by the relation,
1
 mv 2
 h  e 
T
max 2 max
… (1)
Now consider the case of electrons being emitted by a photocathode in a vacuum tube, as
illustrated Fig.2. In this case, all emitted electrons are slowed down as they approach the anode,
and some of their kinetic energy is converted into potential energy. There are three possibilities
that could happen.
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i)
The first is that if the potential is small then the potential energy at the anode is less
than the kinetic energy of the electrons and there is a current through the tube.
ii)
The second is if the potential is large enough the potential energy at the anode is larger
than the kinetic energy and the electrons are driven back to the cathode. In this case,
there is no current.
iii)
The third case is if the voltage just stops the electrons (with maximum kinetic energy
Tmax) from reaching the anode. The voltage required to do this is called the “stopping
potential" (V0).
Fig. 2. A schematic of Photoelectric effect set up
Therefore,
eV  h  e 
0
… (2)
h
V   
0 e
… (3)
The present experimental set-up comprises of a high-vacuum photocell, half of which is coated
with “Potassium” (metal) acting as cathode. The annular anode lies opposite to the cathode. The
electrons which are ejected (at cathode) due to excitation by incident photons, reach the anode.
This leads to a potential difference (negative) between the anode and the cathode. After a short
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charging time, the potential difference (Voltage) reaches a limiting value (U) when no electron can
further reach the anode. “U” is the stopping voltage. Since, the anode and cathode surfaces are
different, an additional contact potential “A” comes into the picture which simply gets added to the
work function “”. So, Eq. (3) can re-written as
h
V       A
0 e
… (4)
Although invisible, the ultraviolet light can be seen on the white reflective mask of the h/e
apparatus, which is made of a special fluorescent material. Ultraviolet line will appear as blue.
The violet will also appear bluish.
Experimental Procedure:
1. Place the Hg lamp and photocell at the opposite ends of the optical bench and the
diffraction grating in the middle on turning knuckle. Keep the vertical slit close to the lamp
and a convex lens in between the slit and the grating. Also position an empty slide holder
just behind the grating on the photocell side. Align both the arms of the bench in a straight
line.
2. Turn on the Hg-lamp (it may take 10-15 mins. to light up) and connect the photocell unit to
the “Measuring amplifier” with a BNC connector. Keep the photocell shutter closed all the
time except while taking readings, of course.
3. For the universal measuring amplifier, select the following settings: (a) electrometer
resistance Re > 1013 Ω, (b) amplification = 100 and (c) time constant =0. Connect a digital
multimeter to the output of the amplifier. The voltmeter range in multimeter is set at 0-2 V
dc.
4. When the Hg-lamp is shining brightly, diffraction pattern (due to the grating) can be
observed in the plane of photocell on holding a piece of white paper on both sides of the
central “white” maximum.
We name them “left spectrum” and “right spectrum”
respectively depending on the side they lay with respect to the Hg-lamp. Position the
convex lens such that it brings the central maximum sharply focused on the location of the
photocell’s entrance diaphragm.
5. Adjust the width of the slit such that the width of the slit image (on the photocell’s entrance
diaphragm) is approximately 1 cm.
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6. Holding the lamp-arm fixed, start turning the photocell arm so as to superimpose the violetcolour (404.6 nm) slit image of the “left spectrum” on the photocell’s entrance diaphragm.
7. With the shutter still closed, discharge the “entrance capacitor” by pressing down the
discharge button and simultaneously adjust the offset knob to show 0 V output in the
multimeter.
8. Keeping the discharge button pressed, open the shutter, make sure the colored slit image is
indeed incident on the photocell entrance and then release the discharge button.
9. Wait till the multimeter voltage reading becomes steady and then record the photocell
voltage U corresponding to the incident wavelength.
10. Once the recording is done, close the shutter, turn the bench further for the next wavelength
and repeat the above steps 6-9. For the yellow line (578 nm), the UV line from the second
order diffraction can contaminate the readings. So place the 525 nm filter in the empty
slide holder to fend off UV from entering the cell.
11. Repeat the step 6-9 (for all the wavelengths) for the “right spectrum”.
12. Repeat the above steps 4-10 for at least another Hg-lamp-grating distances.
13. Plot photocell voltage U vs. frequency ν and determine Planck’s constant h from the slope
of the graph.
Observations:
Table 1
Lamp‐grating Wavelength distance (cm) (nm) … … 404.6 435.8 494.0 546.1 578.0 404.6 435.8 494.0 546.1 578.0 Last updated December 2013, NISER, Bhubaneswar
Frequency (Hz) Photocell Voltage (U) (Right‐side spectrum) Photocell Voltage (U) (Left‐side spectrum) Photocell Voltage (U) (Average spectrum) 7
Precautions:
1) The photocell shutter should usually remain closed except while taking readings
(measuring “U”).
2) Under no circumstances, the photocell should be opened or directly exposed to bright light
as it may damage the photocell.
3) Since, the aperture width of the photocell is 1 cm, the slit width should be correctly
adjusted to make the slit image (at the photocell) to be very close to 1 cm for obtaining
good results.
4) After opening the photocell shutter, wait for at least 1-2 minutes before taking a reading.
5) Be careful and slow while rotating the photocell arm of the optical bench for
superimposing the slit image on the photocell’s diaphragm.
References:
1. Evans, R. D. (1955). The Atomic Nucleus. Malabar, Fla.: Krieger. p. 712.
2. Arthur Beiser (2003), Concept of Modern Physics, 6th edition, p.62-66.
th
3. Modern Physics, (Tipler & Llewellyn, 4 ed.) Chapter 3, pp. 141–147.
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EXPT# 02: The Franck-Hertz Experiment with Hg-tube:
Inelastic Scattering of Electrons by Atoms
Introduction:
Franck and Hertz described the first observation of quantized excitation in 1914; one year
after Bohr published his theory of the hydrogen atom with its concept of quantized energy states.
They discovered that electrons moving through the Hg vapour with an energy equal to or greater
than a certain critical value (4.9eV) can excite the 253.6 nm line of Hg. Electrons with less than
the critical merely bounce off elastically when they collide with Hg atom and fail to excite any
electromagnetic radiation at all. This experiment provided crucial evidence in favour of Bohr
Theory.
Objective:
Study of quantized excitation of Hg atoms by inelastic scattering and Determine the
excitation energy E from the positions of the current strength minima or maxima by difference
formation.
Description:
This experiment is set on the principle of excitation of Hg atoms using an Hg vapour filled
triode valve, called Frank-Hertz Hg tube. The triode valve consists of following three electrodes
and a drop of Mercury (Fig.1).

A Cathode which emits electron when raised to a temperature of several hundred degrees
by application of a voltage UH to the heater filament.

A Grid which is set at a positive potential Vgc relative to the cathode so that the electrons
emitted by the cathode are drawn towards it.

An Anode, which is connected to an ultra sensitive electrometer for measurement of anode
current. Usually it is maintained at a negative potential Vret relative to the grid so as to
retard the electrons.
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Figure 1: Frank-Hertz tube filled with Hg vapour.
Accelerating Voltage
Anode
Current
(A-C)
Ve
Ve
Vret
Figure 2: Plot of Anode Current and Accelerating Voltage (Vgc between grid and cathode) in the
idealized situation. A, C are the work function for metals of cathode and anode respectively, Ve
is the excitation potential, Vret is the retarding potential between grid and anode.
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Equipments:

Franck Hertz operating unit

Franck-Hertz tube filled with Hg.

Franck-Hertz oven.

Ni-Cr-Ni Thermocouple

5-pin connecting cable, shielded BNC cable, RS 232 data cable.

PC with Windows 98 (or higher), Franck-Hertz Measurement Software.
Theory:
The cathode heated by the filament emits electron in a process called thermionic emission
in which electrons near the top of the Fermi surface in the metal penetrate the potential barrier at
the surface and escape. The emitted electrons have a distribution of kinetic energies which is
approximately a Maxwell-Boltzmann distribution with a mean energy E0  kBT where T is the
cathode temperature and kB is the Boltzmann’s constant. In the steady stated with the grid at a
positive potential relative to cathode the emitted electrons form a cloud of negative charges. This
created an electric field forcing lower energy electrons back to the cathode and suppress the
current to which is called space charge limited current. At room temperature the vapour pressure
of Hg is low and probability of collision of an electron with an Hg atom is also low, which gives
rise to a mean free path of electron of the order of the size of the tube. Usually one sets the Anode
at a voltage slightly negative compare to the grid so that if the electron is not energetic enough it
cannot reach the anode. At room temperature, however most of them will reach the anode which
shows up in the anode current.
As we increase the temperature the vapour pressure increases and the mean free path of the
electron decreases so that the probability of collision becomes large. In this case, if we keep on
increasing Vgc, when the Vgc  4.9V kinetic energy of some of the electrons will be sufficient to
excite the valence electron of Hg to the first excited level 6 3P1 by inelastic collision. Those
electrons, which undergo collision, will loose energy in this process and cannot reach the anode
which shows up in a sudden decrease in anode current. As we increase the Vgc further the anode
current will keep on increasing again as more and more electrons will reach the anode. When Vgc
 24.9V kinetic energy of some of the electrons will be sufficient to excite two Hg atoms.
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Consequently it will loose energy in the process and cannot reach the anode. So we will get one
more sudden decrease in anode current.
Let us assume the following idealized situation:

All electrons emerge from cathode with zero velocity.

Number of electrons emerging from the cathode is independent of Vgc.

Energy of an electron does not change under a collision with a Hg atom unless the Hg atom
gets excited.

All electrons pass through the grid with energy E less than E < eVret are collected by the
grid while those with energy E > eVret are collected by the anode.
All these conditions are inaccurate to varying degrees.
However, in this idealized
situation if we plot the anode current IA vs Vgc we will get the square waves (fig-2). The
separation between successive current minima (maxima) will be excitation potential of Hg. The
width of the minima is determined by the retarding potential between grid and anode Vret. The
difference between the first drop of current and excitation potential of Hg is difference between
work functions of cathode and grid metals. In reality, the plot differs considerably from this
idealized situation.
If we assume both grid and anode as plane parallel electrodes, when the temp. is low, the
mean free path is large compare to any length scale in this tube and electron’s motion is ballistic.
Electrons collected by the grid, then, is proportional to fraction of the area covered by the grid
wire. When temp. is high the mean free path is very small, even comparable to the diameter of the
wire, electron orbits jitter along the electric field line and most regardless their energy they are
mostly intercepted by the grid as most of the lines and there.
Note that ground state of Hg is 1S0 and the lowest excited state of Hg is 6 3P0, which is
metastable of lifetime  105 times that of ordinary allowed transition. As the electron accelerates
towards the grid they reach a position where they have sufficient energy to excite the 6 3P0 state
and will do so. Because this excited atoms decay slowly, their number builds up to the point
where some of the electron-mercury atom interactions become elastic collisions off the excited
atoms. The next excited state is 6 3P1 and it is not metastable. This later excited atoms decay with
emission of a 253.6 nm photon. Franck and Hertz detected these photons through the window of
the glass tube. Having measured the threshold voltage V at which the photons appeared they
derived a value for Planck’s constant h/2 = (eV/c)λ which agreed with the values previously
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obtained by Planck Einstein and Bohr from Blackbody radiation, Photoelectric effect and
Hydrogen spectrum respectively. This was a striking confirmation of new quantum theory.
Set-up and Procedure
1. Set-up the experiment as shown in Fig.3 and follow the following procedure.
2. Connect the Hg tube to the Frank-Hertz control unit with the 5-pin connecting cable. Make
sure that plug labeling matches with the socket labeling on the plate.
3. Connect the temperature sensor to the Hg tube by leading the tip of the probe through the
opening in the Franck-Hertz oven and positioning it at the height of the cathode. Plug in
the oven connecting cable to the socket in the control unit. Set the rotary switch at the
value of 6.
4. Use the connecting cords supplied with
the Frank-Hertz operating unit to connect
it to the AC mains supply (230V).
Operate the mains switch at the back of
the instrument to switch it on.
5. Turn on the operating unit using on/off
switch.
Set the ‘function’ to ‘Manual’
using the push button.
Figure 3: Set-up for the Frank-Hertz experiment.
6. Set Vret = U2 = 2V, Vfilament = UH = 6.3V, T = 1200C. Waits till oven reaches the desired
temperature 1200C. Once that is reached change the Vgc = U1 in steps of 0.5 volt and note
IA. Plot IA vs. U1 curve.
7. After setting all the parameters, switch on the ON/OFF switch before taking the readings.
8. If the current is too high then the operating unit will interrupt the measurement
automatically after 7 second to protect the unit from being damaged. At low temp. it is
hard to get sufficient number of peaks as the voltage cannot go all the way to 60V. In order
to avoid discharges decrease the heating voltage UH and decrease the retarding voltage U2
if required.
9. Analysis the curve to obtain explicit values of the maxima and minima of the curve.
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10. Repeat the measurement for T = 150 0C and T = 175 0C keeping the other parameters
constant.
11. Set the temp. at T = 175 0C and repeat the measurement for two more values of retarding
voltages U2 = 1V and U2 = 1.5V.
12. After all measurements, switch the oven off and leave it at least 30 minutes to cool down
before further operation.
13. The excitation energies of mercury atoms can be determined from the distance between
minimum values. Typical results obtained are 4.9 V for Hg atoms.
14. Print out the curves obtained with different temperatures and retarding voltage. Make the
Table given below. Compare them and comment on differences among them and with the
one given in idealized situation.
15. Do the error analysis in measuring quantized excitation energy and explain the source of
error during the measurement.
Once you have the data obtained in manual mode, you can verify and compare your result by
collecting the data using a PC. Then follow the following steps:
16. Connect the operating unit to the computer with an RS-232 cable.
17. Start the measure software and call the Franck-Hertz measurement programme. A screen
(Fig.4) appears with typical values of parameters with which a measurement curve can be
successfully recorded.
18. Set Vgc = U1 = 60V, Vret = U2 = 2V, Vfilament = UH = 6.3V, T = 1200C. and click continue.
The software automatically carries out the essential steering and waits till oven reaches the
desired temp. 120 0C. Once that is reached it will plot the IA vs. Vgc curve (Fig.5).
19. The repeat the same procedure 7-10.
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Observation:
Table.1: For current and voltage plot at different temperature
Temperature
Kinetic energy U1 Current,
(oC)
(in Volt)
IA
(A)
120
150
175
Table 2: Make a table to conclude all the temperature and retarding voltage range.
Kinetic
energy
(in Volt)
Retarding
Oven
U1 Voltage U2 (in temperature
Volt)
Excitaion
Eavg
energy E (eV)
(eV)
T (oC)
Figure 4 show the typical input values of measuring parameters in the computer screen.
Figure 5 shows the typical Frank-Hertz curve recorded with T=175oC at U2=2V.
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Figure 4: Measuring parameters
Figure 5: Example of a Frank-Hertz curve recorded with T=175oC at U2=2V.
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PRECAUTIONS:
1. Do not set the temperature above 1800C, the Franck-Hertz tube may get damaged. Do not
put other devices in the surrounded area (20cm) of the oven.
2. Do not cover the control unit ventilation slits.
3. Do not operate any high-frequency emitters (such as radio, mobile phones, etc.) in the
immediate vicinity of the instrument.
4. When the bimetallic switch switches the oven on and off, there is a change of load on the
AC mains, causing a small change in the set acceleration voltage. This should be noted if
the switching takes place just when the curve is being recorded.
5. Due to oven temperature variations slightly different levels of collection current may be
obtained for repeated measurements at the same acceleration voltage. However, the
position of the maxima remains unaffected.
6. The instrument should be properly earthed. Following a blackout failure operate the on/off
switch for reset.
References:
1. American Journal of Physics, 56(8), August 1988.
2. D. Halliday and R. resnick: Fundamental of Physics, New York, John Wiley, 3rd edition
1988, pp. 491-492.
3. R. Eisberg and R. Resnick: Quantum physics of Atoms, Molecolus, Solids, Nuclei and
Particles, pp 107-110 (F-H effect in Hg), pp 407-409(contact potenstial, thermionic
emission).
4. D. W. Preston and E. R. Dietz: the art of Experimental Physics, Experiment 6, pp 197208.
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EXPT# 03: Study of Hydrogen Spectra (Balmer Series) and
determination of Rydberg’s constant
Introduction
In the 19th Century, much before the advent of Quantum Mechanics, physicists devoted a
considerable effort to spectroscopy trying to deduce some physical properties of atoms and
molecules by investigating the electromagnetic radiation emitted or absorbed by them. Many
spectra have been studied in detail and amongst them, the hydrogen emission spectrum which is
relatively simple and shows regularity, was most intensely studied.
Objective
i)
ii)
To measure the wavelengths of visible spectral lines in Balmer series of atomic
hydrogen
To determine the value of Rydberg's constant
Theoretical Background
According to Bohr's model of hydrogen atom, the wavelengths of Balmer series spectral lines are
given by
1 
1
 Ry  2  2 

m 
n
1
… (1)
where, n = 2 and m = 3, 4, 5, 6 … and Rydberg’s constant R y is given by
e 4 me
R y  2 3  1.097  107 m 1
8 0 h c
… (2)
where ‘e’ is the charge of 1 electron, ‘me’ is mass of one electron, ‘0’ is permittivity of air = 8.85
 10-12), ‘h’ is Planck’s constant and ‘c’ is velocity of light.
The wavelengths of the hydrogen spectral emission lines are spectrally resolved with the help of a
diffraction grating. The principle is that if a monochromatic light of wavelength  falls normally
on an amplitude diffraction grating with periodicity of lines given by ‘g’ (= 1/N, where N is the
number of grating lines per unit length), the intensity peaks due to principal maxima occur under
the condition:
g sin   p
… (2)
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where ‘’ is the diffraction angle and p = 1, 2, 3, … is the order of diffraction.
In the first part of the experiment, the grating constant ‘g’ is determined by measuring the
diffraction angles for the known spectral lines of a mercury (Hg) spectral tube (Mercury-vapour
lamp). The Hg spectral tube is then replaced by a hydrogen (atomic) spectral tube, in which, H 2 is
converted into atomic hydrogen due to collision ionization. The electrons in H atoms are excited to
higher energy levels through collisions with other electrons. When these electrons return to lower
energy levels, the atom emits electromagnetic radiation of discrete frequencies in various spectral
ranges. Balmer's series spectral lines fall in ultraviolet and visible ranges and the latter
wavelengths are determined in this experiment by measuring the corresponding diffraction angles.
Usually, only first order diffraction is studied, for which the value of ‘p’ in Eq. 2 is taken to be
unity.
Experimental Set-up
The experimental set-up is shown in Fig. 1. Hydrogen or mercury spectral tubes connected to a
high voltage power supply are used as the source of light. The spectral tube is fixed between two
high voltage electrodes. A grating and a spectrometer will be used to analyse different spectra.
First, we will use mercury source to determine the grating element (g) and then using this value of
g we will determine the unknown lines of Balmer series of hydrogen spectra.
High Voltage Power Supply: We use two designated power supplies for Hydrogen and mercury
sources. For hydrogen source, the electrodes are connected to an in-built compact power supply.
For mercury source the power supply (PHYWE make) and electrodes are separate. Please take
special care while using this power supply. The main switch of this high voltage power supply is at
the rear panel. There are three sockets provided on the front panel which can be used to get an
adjustable voltage up to 10 kV or ±5 kV. The corresponding LEDs identify the sockets from which
the output voltage is drawn. The 3-position knob selects the output voltage sockets (top and
centre/top and bottom/centre and bottom) and displays the corresponding voltage. A voltage
control knob can be used to set the desired voltage across any pair of sockets. The Earth socket is
connected via the line cord. It can be used to earth any of the three sockets, if required.
CAUTION: DO NOT TOUCH HIGH VOLTAGE ELECTRODES WHICH HOLD THE
SPECTRAL TUBE, WHEN POWER SUPPLY IS ON!
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Hydrogen source
Mercury source
Figure 1 – Experimental set-up
Procedure
A. Adjusting the spectrometer:
Follow the support manual for spectrometer provided in the appendix for basic adjustment of
spectrometer. Determine the vernier constant of the spectrometer. Fix the grating on the prism
table. Do not disturb the spectrometer henceforth throughout the experiment.
B. Installing the Hg spectral tube:
1. Make sure that the power supply is switched OFF and the cords connecting the electrode to
the power supply are disconnected from the power supply.
(THE SPECTRAL TUBE MUST BE INSTALLED, REMOVED OR CHANGED
ONLY IN THE PRESENCE OF THE INSTRUCTOR!)
2. Take out the Hg spectral tube carefully, holding it on the side which has a glass notch.
Gently place the tube inside its metallic cover so that the slot on the cover rests on the
notch. Secure the pin at this end of the tube in a hole in the lower electrode. Loosen the
upper electrode, so that the upper pin of the tube can go into the hole in the upper electrode.
Then, tighten the upper electrode in this position. The small window of the cover should be
in the front. If required, loosen and slightly adjust the orientation of the vertical rod holding
the electrode assembly. The final arrangement should not be disturbed throughout the
experiment.
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3. Connect the electrode cords across the top and centre sockets of power supply and select
the extreme left position for 3-position knob. Do not switch ON power supply.
C. Studying the Hg spectrum:
1. Bring in the Hg source close to the collimator of the previously leveled spectrometer.
2. Ensure that the voltage control knob is minimized. Then switch ON the power supply and
apply a voltage of about 5 kV by adjusting the voltage control knob.
3. Look through the telescope to notice the three first order spectral lines of Hg (yellow, green
and blue) on both sides of the direct image of the slit at the center. Make the spectral lines
vertical by turning the grating slightly in its plane.
4. Note down the positions of the cross wire for each line on one side using the two verniers
on the spectrometer. Use a torch, if needed, to read the verniers.
5. Repeat the above step by turning the telescope to the other side too. Determine the
diffraction angle,, for all the three spectral lines of Hg spectrum. Using the spectral data
of Hg given below, calculate g.
6. Minimize the output voltage and switch OFF power supply. After 1min, disconnect the
cords from power supply.
7. In presence of the instructor/lab operator, loosen the upper electrode and remove the Hg
tube. Remove the metallic cover and place the tube in its box.
8. Remove the electrodes also to make the space free in front of the collimator.
Spectral data of Hg Colour
λ /nm
Transition
yellow
581 ± 1
6 1D1 → 6 1P1
green
550 ± 1
7 3S1 → 6 3P1
green
494 ± 2
8 1S1 → 6 1P1
blue
437 ± 2
7 1S → 6 1P1
6 3D1 → 6 1P1
D. Installing the hydrogen tube and studying its spectrum
1. Make sure first that the power supply for hydrogen tube is switched OFF. Take out the
hydrogen spectral tube and in presence of the instructor/lab operator install it carefully
between the two electrodes provided in the housing. Since the tube has no external
covering take extreme care not to touch it when it is ON.
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2. Bring in the hydrogen source to the front of collimator. Then switch ON the power supply.
Repeat steps C.3 to C.5 (mentioned above) and note down the positions of the cursors for 3
spectral lines (red, green and violet) of the hydrogen spectrum.
3. Using the value of g determined earlier, calculate the wavelength of each of the spectral
lines.
4. Remove hydrogen spectral tube from the electrodes and place it safely in its box.
Observation
Table 1: Determination of g
Colour/
Left side
λ(nm)
Vernier 1(deg)
MSR
VSR
Right side
Vernier 2(deg)
TOTAL
MSR
VSR
Vernier 1(deg)
TOTAL
MSR
VSR
Vernier2(deg)
TOTAL
VSR
MSR
Vernier
Vernier
1
2
Avg.
2θ(deg)
2θ(deg)
θ(deg)
g
TOTAL
Mean value of g =-------
Table 2: Determination of spectral lines of hydrogen
Left side
Colour/
Vernier 1(deg)
Line/
Right side
Vernier 2(deg)
Vernier 1(deg)
Vernier2(deg)
Literature
Value (nm)
MSR
VSR
TOTAL
MSR
VSR
TOTAL
MSR
VSR
TOTAL
MSR
VSR
Vernier
Vernier
1
2
Avg.
λ
2θ(deg)
2θ(deg)
θ(deg)
(nm)
TOTAL
Red/Hα/656.28
Green/Hβ/486.13
Violet/Hγ/434.05
Results and analysis
1. Assign appropriate values of n and m (n = 2 and m = 3, 4 ...) to each  (average value).
Tabulate the values of n and m, the corresponding values of 1 / n 2  1 / m 2  and 1 /  .
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2. Plot 1 /  vs. 1 / n 2  1 / m 2  on a graph sheet. Indicate the error bars of 1 /   by
calculating 1 /     in each case. Indicate n and m for the three data points on the
graph.
3. Draw the linear graph. From the slope of the graph and the error in the slope, determine the
value of Rydberg's constant and the corresponding random error. Write the final result with
its uncertainty.
Precautions
1. Do not touch the high voltage electrodes which hold the spectral tube, when the power
supply in ON.
2. Handle the spectral tube with utmost care. Hold it at notch side and not it in the middle.
3. Never touch the surface of the grating by hand. Always hold it from the sides.
4. Do not change the positions of the spectrometer and the spectral tube throughout the
experiment.
5. Always make sure that the voltage control knob of power supply for Hg source is
minimized, before switching it ON.
6. Switch OFF power supply before making any changes in the spectral tube arrangement.
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23
EXPT#04: Study of emission spectra of metals using constant
deviation spectrometer
_________________________________________________
Introduction:
An instrument used to study the spectra with unaided eye is called spectroscope or spectrometer.
When it is used to photograph the spectrum it is called spectrograph. A constant deviation
spectrometer got its name due to the fact that it uses constant deviation prism or Pellin-Broca
prism.
Objective:
(i)
Calibrate the C.D.S using a calibration source
(ii)
Determine the weave length of the unknown spectra of the given metals in the arc
lamp source.
Apparatus:
The
constant
deviation
spectrometer
(C.D.S),
The
calibration
source
(sodium/mercury lamp), D.C.Power supply, the arc stand, the metals (Copper, Brass, etc.),
Spirit level.
Theory:
When refraction through a prism takes place in such a
manner that the angle of incidence is equal to the
angle of emergence, the refracted ray will be parallel
to the base of the prism (see Fig. 1). The ray is
symmetrical under these conditions. It can be
mathematically proved that when the above
conditions are satisfied for a particular value of i, the
deviation suffered by the light ray is minimum and
the angle of deviation is known as the angle of
minimum deviation δm. For any other value of i, the
value of δ increases.
Figure 1: Angle of deviation in ordinary prism
Constant deviation prism
The construction of constant deviation prism is a single piece but can be considered as composed
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24
of two 30° prisms, PQR and QST along with the reflecting prism PRS (see Fig. 2). AB is an
incident ray and i is the angle of incidence. For certain i BC is normal to PR and totally reflected
at PS and undergoes deviation of 90°.
Since
m PQT = 90º and m BCD = 90º
(1)
m QBC + m QDC =180º
we have,
(2)
But, since
m QBC = 90º + r and m QDC = 90º - i ,
(3)
Therefore,
(90º +r) + (90º - i ) = 180º .
(4)
Thus r = i and emergent ray is perpendicular to the incident ray (this can be easily proved
from the geometry of the figure). Two prisms PQR and QTS can be considered as a single prism
of 60°. When the angle of incidence is equal to the angle of emergence and the angle of deviation
is
90°,
a
ray
would
be
passing
through
a
position
of
minimum deviation. This principle is used in constant deviation spectrometer.
Figure 2: Constant deviation prism
Experimental set up:
The schematic of constant deviation spectrometer set up is shown in Fig.3.
The collimator and the telescope are fixed and the axes are perpendicular to each other. The prism
table can be rotated about the vertical axis using a drum which is attached to the table. The head of
the drum is calibrated for the wavelength and thus the wavelength can be measured directly. When
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the light is incident on the prism the prism table can be rotated till the angles of incidence and
emergence are equal. The pointer seen in the field of view of telescope can be used for the
measurement. After clamping the prism the drumhead is rotated to rotate the prism table and the
desired wavelength is measured.
An ordinary prism and a spectrometer can be used for this task, but the process is time
consuming. The adjustment of minimum deviation and if it is disturbed, resetting is troublesome.
In case of constant deviation spectrometer, if the prism is disturbed it can easily be reset by using a
source of known wavelength.
Figure 3: Experimental set up for Constant Deviation Spectrometer
PROCEDURE:
1. Level the constant deviation spectrometer by means of a sprit level and focus the telescope.
2. Place the constant deviation prism on the prism table so that its 90˚ vertex faces towards
the objective of the telescope.
3. The drumhead is calibrated using known wavelength of a calibration source. The source is
placed in front of the collimator lens.
4. For sodium source the drum is rotated so that it reads 5890 Å, the known value of Na
yellow line. The spectrum is sought for by looking through the telescope. It is brought on
the pointer crosswire by slightly rotating the prism this way or that way.
5. Once the spectral line coincides with the pointer, clamp the prism. Thus the CDS is
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26
calibrated to measure any unknown wave length.
6. Then replace the calibration source by the arc source using a particular metal arc of
interest.
7. The D.C.power supply is connected to the arc stand holding the pointed metal arc one over
the other. Switch ON the power supply and observe the arc begins to glow.
8. The spectrum is observed in the CDS. Adjust the drum head to make the pointer coincide
on each of the spectral lines and read the characteristic wavelength of the different lines
emitted by the metals directly.
9. Compare the values of spectral lines obtained for different metals with the literature values.
PRECAUTION:
1. The arc points or the holders should not be touched as they carry high voltage.
2. To start the glow the two pointer arcs should be brought very close, nearly to touching position
and after the glow a minimum gap is maintained to avoid excess load on the power supply.
3. After taking readings, allow the metal rods to cool down before changing to another pair of
rods.
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EXPT#05: Interference of light using Fresnel’s Bi-Prism and Mirror
Introduction:
If two coherent beams of lights are made to cross each other in the region of crossing where
both beams are present at once, the resultant amplitude or intensity may be very different from the
sum of their intensities. The modification of the intensities obtained by superposition of two beams
is called interference. When the intensity is greater (less) than the sum of the two intensities it is
called constructive (destructive) interference. This is difficult to observe because of small
wavelength of light. The first person successfully demonstrated interference of two beams was
Thomas Young in 1801. This established the wave nature of the light.
After double-slit experiment, objections were raised that the alternate dark and bright fringes
may appear due to some complicated modification of propagation of light near the edges of the
slits and so this is not true interference. Therefore the wave theory of light could be questioned.
Augustin Fresnel brought forward new experiments in 1814-15 in which interference was
demonstrated in a way which was not open to this criticism. Since any physical slit would have
edges he used virtual slit.
Objective:
i) Study of interference pattern due to Fresnel’s bi-prism and mirror.
ii) Measurement of wavelength of light from the interference spectrum of Fresnel’s bi-prism and
mirror.
Apparatus:
(1) Optical Bench (2) Fresnel's Bi-Prism (3) Prism table with holder (4) Fresnel's mirror
(5) Lens L1 (f=20mm) (6) Lens L2 (f=300mm) (7) He-Ne Laser source (1 MW) (8)
Measuring tape (9) Screen (10) Ruled paper.
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Theory :
Fresnel’s Bi-prism: A schematic diagram of the bi-prism experiment is shown in Fig.1. The two
prisms refract the light from the source into two beams which overlap on the screen and produce
interference pattern. If we use a photographic plate we will obtain a picture like Fig 2.
Figure 1: Diagram for interference by Fresnel’s Bi-prism.
Figure 2: Interference pattern using Fresnel’s Bi-prism.
The wavelength of the light beam can be determined from the width of interference fringes
produced on the screen. If u and v are the distances of the source and screen from the biprism and d is the distance between two virtual images S1 and S1 and x is the fringe width
the wavelength of light is given by

 x.d
uv
(3.1)
Due to virtual nature of the sources it is not possible to measure the separation
between the sources directly. One uses lens of focal length f to produce sharp real images
on the screen as shown in fig.3. if u1 and v1 are the object –to-lens and image-to-lens
distances respectively, then they are related by
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1 1 1
 
u1 v1
f
( 3.2)
If d is the separation between two real images on the screen and b is the separation between
two virtual sources then we get
d u1
  d  b(u1 / v1 )
b v1
(3.3)
From the above two equations we obtain
d
b. f
v1  f
(3.4)
Figure 3: Images of virtual sources in Fresnel’s Bi-prism Experiments
Figure 4: Interference pattern using Fresnel’ Mirror.
Fresnel’s Mirror: The beams can be brought together in other ways as well. In the arrangement
called Fresnel’s mirror light from a source is reflected by two plane mirrors inclined at a small
angle  . The mirror produces two virtual images of the slit (S1 and S2 in Fig 5. They act in
every respect like the images formed by bi-prism and the interference pattern (Fig 4) is
obtained
in
the
region
BC.
Last updated December 2013, NISER, Bhubaneswar
Note
that
the
angle
subtended
at
the
meeting
30
point of mirrors by the virtual sources is twice the inclination angle of the mirrors.
Procedure
1. Experimental set-up for producing Fresnel's Bi-prism/Mirror is shown in the Fig 6. Place the
Laser on the optical bench at 2crn, Lens L1 (f=20mm) at 23.3cm and a
mount with prism table at 45 cm. In case of Fresnel's Mirror mount it at 43.2cm.
(These positions are· approximate and may need a little tuning to get appropriate
fringes/images.)
2. Place the bi-prism on the prism table and adjust it in such a way that laser light
incidences on the middle of the prism. In case of mirror, adjust the mirror so that
light incidences at a grazing angle and both parts of the mirror are illuminated
equally.
3. Place a screen with ruled paper pasted on it at a distance of 4m or more from the
Laser. The screen should be perpendicular to the optical bench.
4. Adjust the prism by rotating it a little so that interference pattern appears on the
screen. In case of Mirror adjust its orientation and the inclination. Measure width
of 5 consecutive fringes.
5. Place the other lens L2 (f = 300mm) at approximately 60 cm. Adjust the position of
the lens until sharp real images of the virtual sources appear on the screen. Measure
the distance between two images.
6.Repeat the above measurement for several different distances of the screen.
7.
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Figure 6: Experimental set-up for Fresnel's Bi-prism/Mirror
Observation
A. Position of various optical components:
Source
(cm)
Lens L1
(cm)
Lens L2
(cm)
Bi- prism/Mirror
(cm)
Screen
(cm)
B. Measurement of Fringe-width:
No. of fringes
Width of 5 fringes
Initial
Final
Fringe width
Mean fringe width
Difference
C. Measurement of separation between virtual sources:
object-to-Lens Image-to-Lens
distance u1 (cm) distance v1 (cm)
separation between separation between
real images b (cm) virtual
sources
d=b.f/(v1-f )(cm)
Calculation:
Error Analysis:
___________________________________________
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Expt#06: Study of different fringe patterns using Michelson’s
Interferometer
&
Expt#07: Alignment of Fabry-perot Interferometer and study
of the fringe patterns
Objective:
(I)
To adjust the Michelson interferometer to observe interference fringes of equal
inclination and equal thickness.
(II)
To align the Fabry-perot Interferometer and study the fringes
1. Introduction
The Michelson interferometer can be used for observing interference phenomena such as equal
inclination interference, equal thickness interference, white-light interference, precision
wavelength contrast, determine the zero-path difference and measuring refractive index of a
transparent medium slice or air. The Fabry-Perot interferometer is used for observing multiplebeam interference and measuring the fine structure of spectra (e.g. wavelength disparity of
yellow sodium doublet lines).
2. Theory
2.1 Interference
Light has two vectors: an electric field vector and a magnetic field vector, and these two
vectors can be used to model light waves. When two or more beams of light meet in space,
these fields add according to the principle of superposition.
Generally, light beams which originate from separate sources have no fixed relationship. At
any instant there will be points in space where the fields add to produce the maximum field
strength. Because there is no fixed relationship between the oscillations, a point where there is
a maximum at one instant may have a minimum at the next. As the oscillations of visible light
are faster than the human eye can perceive, the human eye averages these results and perceives
a uniform intensity of light.
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If the light beams come from the same source, there is generally some degree of correlation
between the frequency and phase of the oscillations. At one point in space the light from the
beams may always be in phase. So the combined field will always be a maximum and a bright
spot will be seen. At another point the light from the beams may be always out of phase and
minima, or dark spot, will be seen. This phenomenon is called interference.
In 1801, Thomas Young designed a method for producing such an interference pattern.
He allowed a single, narrow beam of light to fall on two narrow, closely spaced slits, and
placed a viewing screen opposite the slits. When the light from the two slits overlapped on the
screen, a regular pattern of dark and bright bands appeared. When first performed, Young's
experiment offered important evidence to the wave nature of light.
Young's slits can be used as a simple interferometer. If the spacing between the slits
is known, the spacing of the maxima and minima can be used to determine the wavelength of
the light. Conversely, if the wavelength of the light is known, the spacing of the slits could be
determined from the interference pattern.
2.2 Michelson Interferometer
In 1881, A. A. Michelson designed and built an interferometer using a similar principle.
Originally Michelson designed his interferometer as a means to test for the existence of the
ether, a hypothesized medium in which light was thought to propagate. Due in part to his
efforts, the ether is no longer considered a viable hypothesis. However, Michelson's
interferometer has become a widely used instrument for measuring the wavelength of light, for
measuring extremely small distances by using a light source with the known wavelength, and
for investigating optical media.
Figure 1 shows a schematic diagram of a Michelson interferometer. The beam of light from the
light source S strikes the beam-splitter BS, which reflects 50% of the incident light and
transmits the other 50%. The incident beam is therefore split into two beams; one beam is
reflected toward the fixed mirror M1, the other is transmitted toward the movable mirror M2.
Both mirrors reflect the light directly back toward the beam-splitter BS. The light from MI is
transmitted through the beam-splitter BS to the observer's eye E, and the other light form M2 is
transmitted through the compensator plate CP and reflected from the beam-splitter BS to the
observer's eye E.
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Since the beams are from the same light
source, their phases are highly correlated.
When a beam expander is placed between
the light source and the beam-splitter, the
light rays spread out, and an interference
pattern of dark and bright rings, or fringes,
can be seen by the observer. In Figure 1,
M2' is the virtual image of M2, and the light
path of the Michelson interferometer can
be seen as the light path of the air plate
between MJ and M2'. The compensator plate CP parallel to the beam splitter BS has the same
thickness and refractive index with the BS. Because the light paths of the two beams are equal,
and
different
light
waves
have
the
same
retardation,
and
it
is
easy for observing the white-light interference.
The forming process of the interference rings is shown in Figure 2. M2' is the virtual image of
M2, and parallel to M1. For simplicity, light source L is at the observer's position. L1 and L2 are
the virtual images of L formed by M1 and M2', and are coherent. Let d be the distance between
MJ and M2', therefore the distance between L1 and L2 is 2d. So, if d  m / 2 m is an integer),
the phases of the light beams from the normal direction of L1 and L2 are the same, but the
phases of the light beams from other direction are not always the same. Light beams from the
points P” and P" to the observer have a path difference 2d cosθ. If M1 is parallel to M2, the two
light beams have the same angle, θ, and are parallel to each other. So, when 2dcosθ = n (n is
an integer), the two light beams form a maximum field strength. For definite n,  and d, the
value of θ is a constant, and the contour of the maximum point becomes a ring. The centre of
the ring is at the bottom in the line of viewing being perpendicular to the mirror plane.
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2.3 Fabry-Perot Interferometer
When one beam of light passes through a plane-parallel plate, it is reflected many times with
multiple-beam interference taking place, and the interference fringes are sharp and bright. That
is the basic principle of the Fabry-Perot interferometer.
In Figure 3, two partial mirrors G1 and G2 are aligned parallel to one another, forming a reflective cavity.
When monochromatic light irradiates the reflective cavity with entrance angle θ, many parallel rays that
pass through the cavity form the transmitted light. The optical path difference between two neighbouring
rays is:
  2nd cos  .
Thus, the transmitted light intensity is:
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1
1'= 1o
1
4R
1  R 
2
sin 2


Where, R is reflectivity, then, I’ varies with   m
I’ becomes maximum, and when
  (2m'1) / 2
I’ becomes minimum.
(m = o, 1, 2…..)
(m’ = 0, 1, 2…)
3. Specifications and Parameters of the set up
Flatness of beam splitter and compensator 0.05 
Travel of moving mirror
Minimum travel reading
1.25mm (travel of fine micrometer: 25mm)
10mm for presetting (coarse micrometer)
0.0005mm
Sodium-tungsten lamp
Sodium: 10W, Tungsten: 15W
Wavelength measurement accuracy
Relative error of 2% for counting 100 fringes
He-Ne laser output
0.7 - [email protected]
Air chamber with gauge
Chamber length of 80mm, gauge: 0 - 40Kpa
Overall dimension
350x350x245mm
Weight
Approx. 17Kg
4. Experimental set up:
The experimental set up can be easily switched between the Michelson and Fabry-Perot
interferometers. It combines both the interferometers on one square base, which is made of
thick steel plate and has a stable rigid-frame.
The schematic of the equipment is shown in Figure 4. On the stage (2), there are two holes for
installing light sources. The expander (3) is installed on a 2-D translation holder which can
slide on a pair of parallel bars. The fixed mirror (4) is reference mirror of the Michelson
Interferometer, and is also adjustable in the normal direction. The beam splitter (5) is plate with
a semi permeable film on the right side. The compensator plate (6) has the same thickness as
the beam splitter (5) and is parallel to (5).The relative position of beam splitter and
compensator has been adjusted before leaving the factory and there should be no need for
adjustment. (7) is the fixed mirror of Fabry- perot Interferometer, and (8) is F-P movable
mirror which is fixed on the movable mirror stage (12) together with movable mirror (10) of
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37
Michelson Interferometer. The movable mirror stage (12) is controlled by the micrometer (9)
and has a maximum travel of 10 mm. When the fine micrometer (11) moves a distance of
0.01mm (resolution), movable mirror on stage (12) moves a distance of 0.0005mm. A ground
glass screen (13) is used to receive the fringes of the Michelson Interferometer, and for
protecting the eye from the laser light.
1. He-Ne laser
2. Slide Stage
3. Beam expander
4. Fixed Mirror M1
5. Beam splitter
6. Compensator plate
7. F-P Fixed Mirror
8. F-P Movable mirror
9. Corage Micrometer
10. Movable Mirror M2
11.Fine micrometer
12. Movable Mirror stage
13. Ground glass screen
5. Procedure
5.1 Michelson Interferometer
5.1.1 Interference Fringes Observation (with He-Ne laser as the light source)
1) Align the He-Ne laser (see Figure 4) so that the output beam is approximately
parallel with the top of the interferometer base and the height of the beam path is
about 70mm above the base.
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38
2) A faint spot (from the laser) should be visible on the movable mirror. Try to get this
spot as close to the centre of the mirror as possible.
3) Adjust the movable mirror until the reflected beam is directed back into the
laser aperture.
4) Then place the ground glass screen in the positioning hole near the fine micrometer.
Two beam spots will be seen on the screen: one comes from the fixed mirror and the
other from the movable mirror. There are also other spots on the screen with less
brightness due to multiple reflections.
5) Position the beam expander into the light path. Be sure to adjust the x-y screws on
the beam expander in order to capture the whole laser beam in the beam expander.
4)
Place a business card or piece of paper in front of the movable mirror and make
adjustments that the expanded beam spot covers both fixed mirror and movable
mirror. Ensure that whilst placing the card or paper in the beam path the mirror does
not get touched.
7) Remove the beam expander and adjust both fixed and movable mirrors (4) and (10)
until the two bright spots coincide with each other at the centre of ground glass screen.
8) Position the beam expander into the light path. A fringe pattern should appear on
the ground glass screen and only slight adjustments of the movable mirror should
be necessary.
5.1.2 Equal Inclination Interference
Now let’s study the different kinds of fringes which are produced by Michelson interferometer.
As shown in the picture above M2’ is the virtual image of movable mirror M2. In the
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39
observer’s field of view, it looks like that the two light beams are reflected from mirror M1
and M2’ and the interference pattern is just like the thin air film between M1 and M2’.
He-Ne laser as the light source
5)Re-produce the interference image as per 5.1.2 which should be similar to (a).
2) Adjust the coarse micrometer such that images (a) to (e) are viewed in
succession.
3) Set the fine micrometer to the middle of the scale (between 10mm to 15mm).
4) Re-adjust the coarse micrometer as close as possible to image ©.
5) Use the fine micrometer to produce fringes of equal inclination.
6) Take pictures of the fringes in a similar way shown in 5.1.2 and submit with
your report.
5.1.3 Equal Thickness Interference
When M1 and M2’ have a very small angle with each other, the fringes or equal thickness
interference can be observed on the ground glass screen.
He-Ne laser as the light source
1) Install the beam expander and He-Ne laser.
2) Adjust the height of the laser to get the interferometer pattern on ground glass screen.
3) Turn the fine micrometer to move the movable mirror in the direction in which the
interference rings are disappearing at the centre, until there are only a few interference rings
left.
6) Adjust the movable mirror a little so that the movable mirror M2’ is tilted relative to the fixed
mirror M1, you will see the interference stripes.
7) Continue to turn the fine micrometer to make the curved fringes move toward their centre.
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40
Some straight bands will appear in succession. These are the fringes of equal thickness.
8)Take pictures of the fringes in a similar way shown in 5.1.3 and submit with your
report.
5.2 Fabry-perot Interferometer
5.2.1 Multi – beam Interference
1) Turn 900 of the interferometer so that the Fabry- Perot interferometer faces towards
the observer (who is at position E’ (see figure 4)).
2) Adjust the micrometer until the distance between G1 and G2 (see Figure 3) is
approx.2.0 mm.
3) Set up a He-Ne laser at the start of the light path of Fabry–perot interferometer.
Adjust the screw behind the G2 to allow the beam spot to coincide on the laser source.
This means the two mirrors are nearly parallel.
4) Place the white card in the observation field. If the He- Ne laser source displays a
comet like tail display on the back of the card, alignment has not been achieved
properly. Fine tune the adjusting screw until the spots coincide.
5) Place the beam expander (BE) and the frosted glass screen (FG) into the
light path as shown below so that the observe sees a series of multi-beam
interference rings. Take pictures of the fringes in a similar way shown in 5.1.3
and submit with your report.
Precautions:
1. Direct eye exposure to laser should be avoided.
2. Observing laser interference fringes by reflecting mirror is prohibited.
_________________________________________________________________________
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41
EXPT# 08: Determination of wavelength of He-Ne laser
using Michelson Interferometer
Introduction:
The Michelson interferometer is historically important for its use by Michelson and Morley in
1887 to provide experimental evidence against the theory of the luminiferous ether. Michelson
subsequently used the interferometer to measure the length of the standard metre in terms of the
wavelength of an atomic spectral line. In 1907 he became the first U.S. citizen to receive the
Nobel Prize in Physics, “for his optical precision instruments and the spectroscopic and
metrological investigations carried out with their aid.”
Modified versions of the Michelson interferometer are still widely used both in research
and technology. Applications include Fourier transform spectroscopy, the testing of precision
optical components and optical fiber communications.
Broadly speaking there are two classes of interferometers:
 Wavefront-splitting interferometers like the Young’s slit interferometer use two or more
apertures to select different parts of an extended wavefront. The radiation from these
apertures is then combined to form an interference pattern. One example of this class is the
Michelson stellar interferometer which was used by Michelson and Pease in 1921 to make
the first direct measurement of the angular diameter of a star (_ Orionis). Modern optical
stellar interferometers and radio synthesis telescopes are examples of this kind of
interferometer.
 Amplitude-splitting interferometers use a partially reflecting mirror (“beamsplitter”) to
divide an incoming beam of light into two beams. These beams can either be recombined
using the same beamsplitter (Michelson interferometer) or a separate beam combiner can be
used (Mach-Zehnder interferometer).
Objective
iii)
iv)
Determine the wavelengths of given He-Ne laser lines
Explain the phenomenon of beam localization and nature of concentric rings
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42
Equipments:
Michelson interferometer,
Laser (He-Ne)
Swinging arm, Lens mounted (f'= +5mm), Lens holder,
Slide mount, optical profile bench, (1=60 cm),
Metal screen (300 x 300 rnrn)
Experimental setup
Construction:
The Michelson interferometer consists of two plane mirrors M I and M2, highly silvered on their
front surfaces to avoid multiple internal reflections and two plane parallel glass plates which
have been cut from a single optically plane parallel plate to ensure the equality of thickness and
the nature of the material. Both the plates are mounted vertically, exactly parallel to each other,
on a heavy frame and are inclined at 45° to the interferometer arm. Plate G has is coated with
silver or Aluminum such that it acts as a 50/50 beam splitter. The mirror M2 is fixed while the
other mirror M is movable and is mounted on a carriage C as shown in figure 2. The carriage has
a precision back and forth movement. During the motion M, remains exactly parallel to its
preceding positions. The mechanism which provides motion to the mirror M consists of a large
drum as shown in Fig.2. The distance travelled by the mirror is 1/10th of the distance moved by
the micrometer screw (lever reduction 1:10).
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Working Principle:
In the Michelson interferometer light from the
monochromatic source is split into two beams by the
half-silvered mirror G, reflected by two mirrors,
which then are reflected off mirrors M 1 and M2 as
can be seen in the schematic representation in Fig 2.
Fig.2:Michelson Interferometer setup
The reflected beams interfere and produce an interference pattern which depends on the path
difference between the two beams.
Fig.3: Formation of circles on Interference.
If we look at the screen D, we see an image of mirror P1 and a virtual image of mirror P2. So, a
point P of the real light source is formed as the points P’ and P" of the virtual light
sources L1 and L2. (See Fig 3.).
When the arms of the interferometer arc equal in length image M2 coincides with M1. If M1
and M2 do not coincide then the distance between them is finite M2M1=d (say). So the path
difference between P’and P" is 2d. If the observer looks into the system at an angle  . Then the
path difference is 2dcos  . The light that comes from M2 goes a rare to-dense reflection and
hence there is a phase change of π. Therefore, the total path difference between the two beams is
given by   2d cos    / 2 . Hence, the condition for obtaining dark fringe is 2d cos   m
and the condition for obtaining a bright fringe is
2dcos  = (2m-1) /2
For a given mirror separation d, wavelength 
Last updated December 2013, NISER, Bhubaneswar
and order m, the angle 
is
44
constant. This means that the fringes are of circular shape. They are called fringes of equal
inclination.
For  =0, the path difference between the interfering beams would be  2 . Consequently, we
obtain a minimum at the coincidence position and the centre of the field will be dark. If one of
the mirrors is now moved a distance  4 , such that the path difference changes by  2 , a
maximum is obtained. If the mirror is moved through another  4 , a minimum is obtained. As d
increases, new rings appear in the center faster than rings already present disappear and
the field becomes more crowded with thinner rings (see Fig. 4).
Fig.4: Formation of fringes
Experimental Procedure:
Adjustment of Michelson Interferometer:
Michelson Interferometer is said to be in normal adjustment when the partially silvered beam
splitter surface G1, accurately bisects the angel between the reflecting mirrors M1 and M2 and
normal to the fringes could be concentric circles. This can be done as follows.........
1. Put the interferometer on a rigid table and level the instrument with three leveling screws
provided at the base.
2. Now put the He-Ne laser, about 50 to 60 cm away from the instrument such that its beam
passes through the pin hole fitted in front of the instrument. Make sure that the laser beam
falls at the middle of the Mirrors M1 and M2 after getting split from beam splitter plate .
3. Make sure that the distances of M1 and M2 are almost equal from .
4. The beam after the reflection will make four spots on the wall or on a screen as shown in the
fig.4. One pair 1 and 2 is formed due to partial reflection at the unsilvered surface of
and
reflection at M1 and M2 respectively. While the other pair 3 and 4 is formed due to partial
reflections at M1 and M2 respectively. Out of these one pair is brighter than the other.
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5. Now mirrors M1 and M2 are tilted carefully such as the two brighter images coincide as
shown in fig 5.
6. Now the instrument is aligned. Introduce the lens in between the laser and pin hole remove
the pin hole out of the path of the beam. See that expanded beam falls on the two mirrors M1
and M2. You will see the fringes on the wall or screen.
7. By using the fine tilt of fixed mirror and motion of the mirror M1, you can adjust the centre
of the circular fringes and can perform the experiments.
8. Do not use the telescope and do not see directly into the laser beam.
Determination of wavelength:
First note the position of the screw gauge for mirror for fringe in the centre. Now move the
mirror through some distance and count the number of bright fringes which appear in the same
spot. The distance travelled by the mirror must be read off on the micrometer screw and divided
by ten (lever reduction 1:10). One can then obtain the wavelength in the following way.
2
2
2
1
)=(
2
,2
2
)λ
1
2
2
Observation and Result:
Initial position of gauge (
SL.NO.
(MM)
= __________ mm
(
)
N
(MM)
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Plot d vs. N. Then, λ = slope/2
Result: The wavelength of He-Ne laser light is determined to be:
Error Analysis: Calculate the error on the wavelength and attach a separate sheet for the
analysis.
Precaution:
1. While assembling and operating the interferometer it is important to remember that
laser beams can cause severe eye damage. Do not look directly into the He-Ne...Laser
beams. Keep your head well above the horizontal plane of the laser beams at all
times. Use white index cards to locate beam spots along the various optical paths.
2. After turning on the laser allow 5 minutes to pass before attempting to make any
adjustments.
3. If you turn off the laser for some reason, wait for 5 minutes before turning it on to
allow it to cool down.
___________________________________________________________________________
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47
EXPT#09: Measurement of the wavelength separation of
sodium D-lines using diffraction grating
Objective: Measurement of the wavelength separation of sodium D-lines using a diffraction
grating and to calculate the angular dispersive power of the grating.
Apparatus: Spectrometer, prism, diffraction grating, sodium lamp with power supply.
Theory
The sodium spectrum is dominated by the bright doublet
known as the sodium D-lines at 589.0 and 589.6 nanometers as
shown in Fig. 1. Using an appropriate diffraction grating the
wavelength separation of these two lines can be determined. A
schematic for diffraction of sodium light (Na-D lines) with a plane
transmission grating is shown in Fig. 2.
Figure 1: Sodium D-lines
Diffraction Grating:
An arrangement consisting of a large number of parallel slits of the same width and separated by
equal opaque spaces is known as diffraction grating. It is usually made by ruling equidistant,
extremely close tine grooves with a diamond point on an optically plane glass plate. A
photographic replica of a plate made in this way is often used as a commercial transmission
grating.
For N parallel slits, each with a width e, separated by an opaque space of width b. the
diffraction pattern consists of diffraction modulated interference fringes. The quantity (e+b) is
called the grating element and N (= 1/ (e+b)) is the number of slits per unit length, which could
typically be 300 to 12000 lines per inch. For a large number of slits, the diffraction pattern
consists of extremely sharp (practically narrow lines) principal maxima, together with weak
secondary maxima in between the principal maxima. The various principal maxima are called
orders.
For polychromatic incident light falling normally on a plane transmission grating the principal
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maxima for each spectral colour are given by
(e+b) sin =  m
(1)
Where m is the order of principal maximum and θ is the angle of diffraction.
Angular dispersive power:
The angular dispersive power of the grating is defined as the rate of change of angle of
diffraction with the change in wavelength. It is obtained by differentiating Eqn. 1 and is given by
d
m

d (e  b) cos 
(2)
Experimental setup:
The actual experimental set up is shown in Fig. 3.
Figure 2: Schematic for diffraction of sodium Na-D lines
Figure 3: Actual experimental set up
PROCEDURE :
1. Follow the support manual for spectrometer provided in the appendix for basic adjustment of
spectrometer. Determine the vernier constant of the spectrometer.
2. Now remove the prism from the turntable. The next step is to adjust the grating on the
turntable so that its lines are vertical, i.e. parallel to the axis of rotation or the turntable.
Moreover, the light from the collimator should fall normally on the grating. To achieve this
the telescope is brought directly in line with the collimator so that the centre of the direct
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49
image of the slit falls on the intersection of the cross-wires. In this setting of the telescope, its
vernier reading is taken; let it be .
3. The telescope is now turned through 90° from this position in either direction so that the
reading of the vernier becomes (+900) or (-900). Now the axis of telescope is at right angles
to the direction of rays of light emerging from the collimator. The telescope is clamped in
this position.
4. The grating of known grating element is then mounted on the grating holder, which is fixed
on the turntable in such a way that the ruled surface of the grating is perpendicular to the line
joining two of the leveling screws (say Q and R).
5. The table is now rotated in the proper direction till the reflected image of the slit from the
grating surface coincides with the intersection of the cross-wires of the telescope.
6. By the help of two leveling screws (Q and R), perpendicular to which grating is fixed on the
table, the image is adjusted to be symmetrical on the horizontal cross- wires. The plane of the
grating, in this setting, makes an angle of 45° with the incident rays as well as with the
telescope axis.
7. The reading of vernier is now taken and with its help, the turntable is rotated through 450
from this position so that the ruled surface becomes exactly normal to the incident rays.
The turntable is now firmly clamped.
8. The final adjustment is to set the lines of the grating exactly parallel to the axis of
rotation of the telescope. The telescope is rotated and adjusted to view the first order
diffraction pattern. The third leveling screw (P) of the prism table is now worked to get
the fringes (spectral lines) symmetrically positioned with respect to the horizontal crosswire.
9. If this adjustment is perfect, the centers of all the spectral lines on either side of the direct
one will be found to lie on the intersection of the cross-wires as the telescope is turned to
view them one after another. The rulings on the grating are now parallel to the axis
rotation of the telescope. The grating spectrometer is now fully to make the measurements.
Do not disturb any of the setting of the spectrometer henceforth throughout the
experiment.
10. Look through the telescope to notice the first order D lines of sodium (yellow lines) on
both sides of the direct image of the slit at the center. Note down the positions of the cross
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wire for each line on one side using the two verniers on the spectrometer. Use a torch, if
needed, to read the verniers. Repeat the above step by turning the telescope to the other
side too. Determine the diffraction angle,, for all the two spectral lines.
11. Take two sets of reading for each D-line and calculate the corresponding wavelength λ1
and λ2 using Eq. 1.
Observation
Number of lines on grating = -------Sodium
Doublet
Grating element = ----------
Left side
Vernier 1(deg)
MSR
VSR
TOTAL
Right side
Vernier 2(deg)
MSR
VSR
TOTAL
Vernier 1(deg)
MSR
VSR
TOTAL
Order, m= 1
Vernier
Vernier2(deg)
MSR
VSR
Vernier
1
2
Avg.
2θ(deg)
2θ(deg)
θ(deg)
λ
TOTAL
D1
θ1=..
λ1=..
D2
θ2=..
λ2=..
Results:
1. Calculate λ1 and λ2 and the uncertainity of the result.
2. Calculate the difference λ2~ λ1 and compare with the literature value.
3. Calculate the angular dispersive power.
PRECAUTIONS:
1. Once the collimator and the telescope are adjusted for parallel rays, their focusing should
not be disturbed throughout the experiment.
2. Once the grating is properly adjusted on the turntable it should be locked.
3. While taking measurements at different positions of the telescope. It must always be in locked
condition.
4. While rotating the telescope arm if the vernier crosses over 0º (360º) on the circular main scale
take the angular difference appropriately.
REFERENCES:
(1) B.L. Worsnop and H.T. Flint, Advanced Practical Physics for Students.
(2) B.K. Mathur. Introduction to Geometrical and Physical Optics.
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51
EXPT# 10: The Velocity of Ultrasonic Waves in liquid by the
Debye-Sears Effect
Introduction:
Acoustic waves in liquids cause density changes with spacing determined by the frequency and
the speed of the sound wave. For ultrasonic waves with frequencies in the MHz range, the spacing
between the high and low density regions are similar to the spacing used in diffraction gratings. Since
these density changes in liquids will cause changes in the index of refraction of the liquid, it can be shown
that parallel light passed through the excited liquid will be diffracted much as if it had passed through a
grating. The experiment can serve as an indirect method of measuring the velocity of sound in various
liquids. The phenomenon of interaction between light and sound waves in a liquid is called the
Debye-Sears effect.
Objective:
1.
To study the diffraction of light by density fluctuations in a liquid and determine the speed
of sound at room temperature using ultrasonic diffraction method.
2.
To determine the compressibility of the given liquids.
Equipments:
1. Radio frequency oscillator fitted with a frequency meter
2. Quartz crystal slab fitted with two leads
3. Spectrometer
4. Glass cell with experimental liquid (kerosene, Toluene, Turpentine oil)
5. Sodium lamp
6. Spirit level.
Theory and evaluation:
Diffraction phenomenon similar to those with ordinary ruled grating is observed when
Ultrasonic waves traverse through a liquid. The Ultrasonic waves passing through a liquid is an
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elastic wave in which compressions and rarefactions travel one behind the other spaced regularly
apart. The successive separations between two compressions or rarefactions travel one behind
the other spaced regularly apart. The successive separations between two compressions or
rarefactions are equal to the wavelength of ultrasonic wave, λu in the liquid. Due to reflections at
the sides of the tank or the container, a stationary wave pattern is obtained with nodes and
antinodes at regular intervals. We are thus dealing and hence having a periodically changing
index of rarefactions which produces diffraction of light according to the grating rule.
If λu denotes the wavelength of sound in the liquid, λ the wavelength of incident light in
air and θn is angle of diffraction of nth order, then we have,
d sin θ n  nλ
In a transparent medium, variations in density correspond to variations in the index of refraction
and therefore a monochromatic parallel light beam traveling perpendicular to the sound direction
is refracted as if it had passed through a diffraction grating of spacing d =λu, Where d is equal to
λu, thus-
λ u sin θ n  nλ
If ν is the frequency of the crystal, the velocity ‘Vu’ of ultrasonic wave in the liquid is
given by,
Vu  ν λ u
Thus, by measuring the angle of diffraction θn, the order of diffraction n, the wavelength
of light, the wavelength of ultrasonic wave in the liquid can be determined and then knowing the
frequency of sound wave, its velocity ‘Vu’ can be obtained.
Compressibility of liquid, K
The speed of sound depends on both an inertial property of the medium (to store kinetic
energy) and an elastic property (to store potential energy):
Vu 
elastic property
inertial property
For a liquid medium, the bulk modulus E accounts for the extent to which an element from the
medium changes in volume when a pressure is applied:
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B 
p
V
V
Here V/V is the fractional change in volume produced by change in pressure P. The sign of V
and P are always opposite. The unit of E is Pascal (Pa). Therefore, the speed of sound in liquid
can be expressed as
Vu 
ν λn
E

sinθ
ρ
 E = Vu 2 = 1/ K
Where, E = Bulk modulus of Elasticity
 = Density of liquid.
K= the compressibility of the liquid
Figure 1: The schematic of the ultrasonic diffraction experiment
Set-Up and Procedure:
1. Switch on the sodium vapor lamp (if it is not on) and wait for 15 minutes to get the
intense light.
2. Check for basic adjustment of the spectrometer. If needed level it taking help of the
support manual for the spectrometer.
3. Place the glass cell containing the experimental liquid (i.e. kerosene oil or others) on the
central part of the prism table.
4. Mount the transducer (quartz crystal in its holder) and dip it exactly parallel in the liquid
near a wall of the glass cell so that the ultrasonic waves produced by the crystal travel in
the liquid in a direction perpendicular to that of the incident light. Connect the leads of
the transducer with the output terminals of the RF Oscillator.
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5. See through the telescope eyepiece so that a sharp well defined image of the slit is seen in
the field of view in the centre of the micrometer scale fitted in the eyepiece.
6. Now switch on the RF Oscillator. Adjust the frequency of the Oscillator to generate the
ultrasonic wave (of the order of ~2MHz) so that it becomes equal to the natural frequency
of the crystal slab. At this stage resonance takes place and diffraction images of the slit
will be seen in the telescope. Note the frequency of the RF Oscillator and maintain it
constant throughout the experiment.
7. Using the vernier scale on the angle display window, measure the angles corresponding
to m = 0, m = 1 and m = 2. Use the data to find out the wavelength of the sodium light.
Observations:
Least Count of Spectrometer = ________
Frequency of Vibrating crystal = ________
Density of liquid
= ________
Table: (Make separate tables for different experimental liquids)
Order
Left of Right of 2θ =
Central
Central
(a –b)
a
a′
b
b′
2θ =
(a′-b′)
Average
2θ
(in ′)
θ
(in ′)
Velocity
(in m/s)
Set-I
2nd order
1st order
Set-II
2nd order
1st order
Set-III
2nd order
1st order
Set-I
Vu
Set-II
Set-III
1st order
2nd order
Mean Velocity = ___________ m/s
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Results and Discussion:
1. Report the mean velocity in each of the liquid.
2. Calculate the Bulk modulus of Elasticity and compressibility for each liquid
3. Estimate the experimental errors, both by relative error and propagation error.
4. Compare the results with data from the literature.
Precautions:
1.
This experiment requires precision in taking readings, especially the minutes in the
spectrometer scale.
2.
Crystal should be exactly to the slit. So that, wave travel perpendicular to incident light.
3.
If the crystal is not parallel to the side walls a good standing wave pattern will not be
obtained & hence diffraction grating will not be formed. As the result the higher orders may
not be of equal intensity on either side of maxima.
4.
Distance of crystal from the wall of the container should be such that these walls sure as
nodal planes.
Note:
1. Velocity of sound in liquids is temperature dependent.
2. From this experiment we are determining the bulk modulus for adiabatic compression
because there is no energy exchanged with the region next to the sound wave. This should
be distinguished from the isothermal bulk modulus.
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EXPT# 11: Study of Polarization by verification of
Malu’s law
Introduction
Linear polarized light passes through a polarization filter. Transmitted light intensity is
determined as a function of the angular position of the polarization filter. From this experiment t
one you can learn about….Electric theory of light, polarization, polarizer, analyzer, Brewster's
law, Malus' law.
Objectives:
1. To determine the plane of polarization of a linear polarized laser beam.
2.
To determine the intensity of the light transmitted by the polarization filter as a function
of the angular position of the filter. 3. Malus’ law must be verified.
Equipments Needed:
1.
2.
3.
4.
5.
Laser, He-Ne 1.0 mW, 220 V AC
Optical profile bench, l = 60 cm
Polarising filter on stem
Photodetector
Digital multimeter
Set-up and procedure:
1. The experiment is set up according to Fig. 1. It must be made sure that the photocell is
totally illuminated when the polarization filter is set up.
2. If the experiment is carried out in a non darkened room, the disturbing background
current i0 must be determined with the laser switched off and this must be taken into
account during evaluation.
3. The laser should be allowed to warm up for about 30 minutes to prevent disturbing
intensity fluctuations.
4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90°
and the corresponding photo cell current (most sensitive direct current range of the digital
multimeter) is determined.
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Fig. 1: Experimental set-up: Malus’ law.
Theory and evaluation:
Let AA' be the Polarization planes of the analyzer in Fig. 2. If linearly polarized light, the
vibrating plane of which forms an angle X with the polarization plane of the filter, impinges on
the analyzer, only the part
EA = E0 . cos 
(1)
will be transmitted.
As the intensity I of the light wave is proportional to the square of electric field intensity vector
E, the following relation (Malus' law) is obtained
IA = I0 . cos2 
(2)
Figure 2: Geometry for the determination of transmitted light intensity.
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Observations:
1. The experiment is set up according to Fig. 1. It must be made sure that the photocell is
totally illuminated.
2. Using a digital multimeter the disturbing background current i0 must be determined with
the laser switched off. This must be taken into account during evaluation.
3. Switch ON the laser. It should be allowed to warm up for about 30 minutes to prevent
disturbing intensity fluctuations.
4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90°
and the corresponding photo cell current (most sensitive direct current range of the digital
multimeter) is determined.
5. Make the table required for angle and the corrected photo current. Identify the intensity
peak and show that the polarization plane of the emitted laser beam has already been
rotated by this angle against the vertical. It may look like Fig. 3 below.
6. Show that the corrected and normalized photo cell current as a function of the angular
position of the analyzer. It may look like Fig. 4 below. Malus's law is verified from the
slope of the line.
Fig3: Corrected photo cell current as a function of the
angular position  of the polarization plane of the analyzer.
Fig. 4: Normalized photo cell current as
a function of cos2 .
Results and Discussion:
1.
2.
Estimate the experimental errors.
Explain different light phenomenon happening during this experiment.
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Appendix: Support manual for prism spectrometer
In some of the optics experiments, we will use a spectrometer. The spectrometer is an instrument
for studying the optical spectra. Light coming from a source is usually dispersed into its various
constituent wavelengths by a dispersive element (prism or grating) and then the resulting
spectrum is studied. A schematic diagram of a prism spectrometer is shown in Fig. 1. It consists
of a collimator, a telescope, a circular prism table and a graduated circular scale along with two
verniers. The collimator holds an aperture at one end that limits the light coming from the source
to a narrow rectangular slit. A lens at the other end focuses the image of the slit onto the face of
the prism. The telescope magnifies the light dispersed by the prism (the dispersive element for
your experiments) and focuses it onto the eyepiece. The angle between the collimator and
telescope are read off by the circular scale. The detail description of each part of the
spectrometer is given below.
Eye piece Focus Knob Telescope Prism Table
Collimator Leveling screws
Leveling screw Verniers Adjustable slit Leveling Focus Knob
screw Height adjustment screw for prism table
Telescope rotation: Fine adjustment screw Clamp screw Circular scale Magnifying glass to read vernier
Prism table rotation: Clamp screw Fine adjustment screw Fig. 1: Different parts of spectrometer
1 Base leveling screws (i) Collimator (C): It consists of a horizontal tube with a converging achromatic lens at one end
of the tube and a vertical slit of adjustable width at the other end. The slit can be moved in or out
of the tube by a rack and pinion arrangement using the focus knob and its width can be adjusted
by turning the screw attached to it. The collimator is rigidly fixed to the main part of the
instrument and can be made exactly horizontal by adjusting the leveling screw provided below it.
When properly focused, the slit lies in the focal plane of the lens. Thus the collimator provides a
parallel beam of light.
(ii) Prism table (P): It is a small circular table and capable of rotation about a vertical axis. It is
provided with three leveling screws. On the surface of the prism table, a set of parallel,
equidistant lines parallel to the line joining two of the leveling screws, is ruled. Also, a series of
concentric circles with the centre of the table as their common centre is ruled on the surface. A
screw attached to the axis of the prism table fixes it with the two verniers and also keep it at a
desired height. These two verniers rotate with the table over a circular scale graduated in fraction
of a degree. The angle of rotation of the prism table can be recorded by these two verniers. A
clamp and a fine adjustment screw are provided for the rotation of the prism table. It should be
noted that a fine adjustment screw functions only after the corresponding fixing screw is
tightened.
(iii) Telescope (T): It is a small astronomical telescope with an achromatic doublet as the
objective and the Ramsden type eye-piece. The eye-piece is fitted with cross-wires and slides in
a tube which carries the cross-wires. The tube carrying the cross wires in turn, slides in another
tube which carries the objective. The distance between the objective and the cross-wires can be
adjusted by a rack and pinion arrangement using the focus knob. The Telescope can be made
exactly horizontal by the leveling screws. It can be rotated about the vertical axis of the
instrument and may be fixed at a given position by means of the clamp screw and slow motion
can be imparted to the telescope by the fine adjustment screw.
(iv) Circular Scale (C.S.): It is graduated in degrees and coaxial with the axis of rotation of the
prism table and the telescope. The circular scale is rigidly attached to the telescope and turned
with it. A separated circular plate mounted coaxially with the circular scale carries two verniers,
V1 and V2, 180° apart. When the prism table is clamped to the spindle of this circular plate, the
prism table and the verniers turn together. The whole instrument is supported on a base provided
with three leveling screws. One of these is situated below the collimator.
Adjustment of Spectrometer: The following essential adjustments are to be made step by step
in a spectrometer experiment: Leveling the apparatus means making (a) the axis of rotation of
the telescope vertical, (b) the axis of the telescope and that of the collimator horizontal, and (c)
the top of the prism table horizontal. The following operations are performed for the purpose.
(i) Leveling of telescope: Place a spirit level on the telescope tube making its axis parallel to that
of the telescope. Bring the air bubble of the spirit level halfway towards the centre by first
turning the two base leveling screws (i.e. leaving the base leveling screw below collimator) and
then turning the telescope leveling screw. Now rotate the telescope through 180° and adjust the
base and telescope leveling screws. Repeat the operations several times so that the bubble
remains at the centre for both positions of the telescope. Next place the telescope in the line with
the collimator and bring the air bubble of the spirit level at the centre by turning the base leveling
2 screw below the collimator. Again check the first adjustment for the previous orientations of
telescope. The axis of the rotation of the telescope has thus become vertical and the axis of the
telescope has become horizontal.
(ii) Leveling of collimator: Remove the spirit level from the telescope. Place it on the collimator
along its length. Bring the air bubble of the spirit level at the centre by adjusting the collimator
leveling screw provided below the collimator. This makes the axis of the collimator horizontal.
(iii) Leveling of the prism table: Place a spirit level at the centre of the prism table and parallel
to the line joining two of the leveling screws of the prism table. Bring the air bubble of the spirit
level at the centre by turning these two screws in the opposite directions. Now place the spirit
level perpendicular to the line joining the two screws and bring the bubble at the centre by
adjusting the third screw. This makes the top of the prism table horizontal.
(iv) Adjusting cross wires and focusing image
Rotate the telescope towards any illuminated background. On looking through the eye-piece, you
will probably find the cross-wires appear blurred. Move the eye-piece inwards or outwards until
the cross-wire appears distinct.
Place the telescope in line with the collimator. Look into the eye-piece without any
accommodation in the eyes. The image of the slit may appear blurred. Make the image very
sharp by turning the focusing knob of the telescope and of the collimator, if necessary. If the
image does not appear vertical, make it vertical by turning the slit in its own plane. Adjust the
width of the slit to get an image of desired intensity.
(v) Optical leveling of a prism: The leveling of a prism makes the refracting faces of the prism
vertical only when the bottom face of the prism, which is placed on the prism table, is
perpendicular to its three edges. But if the bottom face is not exactly perpendicular to the edges,
which is actually the case, the prism should be leveled by the optical method, as described
below:
(a) Illuminate the slit by sodium light and place the telescope with its axis making an angle of
about 90° with that of the collimator.
(b) Place the prism on the prism table with its vertex coinciding with that of the table and with
one of its faces (faces AB in Fig. 2) perpendicular to the line joining two of the leveling
screws of the prism table.
(c) Rotate the prism table till the light reflected from this face AB of the prism enters the
telescope. Look through the telescope and bring the image at the centre of the field of the
telescope by turning the two screws equally in the opposite directions.
(d) Next rotate the prism table till the light reflected from the other face AC of the prism enters
the telescope, and bring the image at the centre of the field by turning the third screw of the
prism table.
(vi) Focusing for Parallel rays by Schuster’s method: This is the best method of focusing the
telescope and the collimator for parallel rays within the space available in the dark room. In
order to focus the telescope parallel light rays are required and this in turn requires a properly
adjusted collimator. For this reason the adjustment of the telescope and the collimator are usually
done together.
3 Schuster's method is based on the fact that the
effect of the prism on the divergence of the beam
is different on opposite sides of this minimum
deviation position (see Fig. 2). The emergent
beam will be less divergent (or more divergent)
than the incident beam as the angle of incidence
is increased (or decreased) from the minimum
deviation value (i.e. as the apex A in Fig.2 is
rotated towards, or away from, the telescope).
This property of the prism can be used to obtain
an accurately collimated beam. The method is
explained below:
Fig. 2: Minimum deviation of light ray
(a) Place the prism on the spectrometer table as shown in Fig.2.
(b) For your prism the angle of minimum deviation is around 50° so set the telescope at an angle
a few degrees greater than this (~55°).
(c) Illuminate the slit of the spectrometer with light from a sodium lamp. Rotate the prism table
and observe the images of the slit through the telescope as it passes through the minimum
deviation position.
(d) Lock the telescope at an angle a few degrees greater than this position.
(e) Turn the prism table away from its minimum deviation position so that apex A moves
towards the telescope and a spectral line is brought into the centre of the field of view of the
telescope. Adjust the focus of the telescope until this line image is as sharp as possible.
(f) Turn the prism table to the other side of the minimum deviation position until the same
spectral line is again at the centre of the telescopes field of view. Now adjust the focus of the
collimator until a sharp image is once more obtained.
(g) Repeat this process until no further adjustment is required. If the same line image is sharply
focused when viewed on either side of the minimum deviation position then the light beam
through the prism is properly collimated.
4