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NATIONAL INSTITUTE OF SCIENCE EDUCATION AND RESEARCH
BHUBANESWAR
SCHOOL OF PHYSICAL SCIENCES
COURSE NAME: FIRST YEAR (SECOND SEMESTER) PHYSICS LABORATORY
COURSE CODE: P-142
COURSE CREDITS: 2
LIST OF EXPERIMENTS
1. Conversion of Voltmeter to Ammeter and vice-versa.
2. Study of Electromagnetic Damping.
3. Determination of the Horizontal Component of Earth’s magnetic field using
a tangent coil galvanometer.
4. Magnetic field variation along the axis of a circular coil and a Helmholtz
coil.
5. Determination of the resolving power of telescope.
6. Determination of Dispersive power of the material of the prism using
spectrometer.
7. Study of Newton’s rings.
8. Laser diffraction and interference.
9. Study of Polarization and verification of Malus’s law.
Conversion of voltmeter to ammeter and vice-versa
Objective
• Convert a given voltmeter to an ammeter of suitable range and calibrate the
ammeter so prepared.
• Convert a given (micro or milli) ammeter to a voltmeter of suitable range and
calibrate the ammeter so prepared.
Apparatus
Voltmeter, (micro or milli) Ammeter, resistance boxes (1Ω – 10kΩ and fractional),
wires, digital voltmeter and milli-ammeter or multimeter, power supply (0–5 volt).
Working Theory
Voltmeter measures voltage drop across resistance by putting it in parallel to
the resistance as shown in Fig 1. The internal resistance of a voltmeter is quite
high (Rm ≫ R) and, therefore, when connected in parallel the current through the
voltmeter is quite small (iv ≈ 0). This keeps the current ir flowing through the
resistance R almost the same as when the voltmeter was not connected. Hence, the
voltage drop (ir R) measured across the resistance by a voltmeter is also almost the
same as the voltage drop without the voltmeter across the resistance.
On the other hand, ammeter measures current through resistance by connecting it
in series with the resistance, Fig 1. An ammeter has very low resistance (Rm ≪ R) and
changes the effective resistance of the circuit only by a tiny amount (R + Rm ≈ R),
not altering the original current by too much. Therefore, the current measured by
the ammeter is about the same as without the ammeter in the circuit.
Rm
iv
V
ir
Rm
R
i
R
A
Fig 1. Schematic diagram of voltmeter and ammeter connections
Conversion of voltmeter to ammeter
Since the internal resistance of a voltmeter is much greater than ammeter, for
conversion to ammeter we need to decrease the voltmeter’s internal resistance by
adding appropriate shunt i.e. resistance in parallel to the meter. Let the range of the
voltmeter be 0 – V0 volt and we convert it to an ammeter of range 0 – I0 Amp.
To calculate the shunt resistance, we need to know the resistance of the voltmeter.
This is done by half-deflection (potential divider) method using the circuit shown in
1
Fig 2(a). Let Rm be the internal resistance of the voltmeter, and when R = 0 the
voltmeter reading is Vm , the current through the circuit is i = Vm /Rm . But when
R 6= 0 and the voltmeter reads Vm /2, the current in the circuit reduces by half
implying i/2 = Vm /(R + Rm ). The voltmeter resistance Rm is given by,
Vm
Vm
=
⇒ Rm = R
2Rm
R + Rm
(1)
Once Rm is determined, the shunt Rsh can be determined by noting that, to get
full-scale reading V0 of the voltmeter we need a maximum current of Im = V0 /Rm .
For full-scale reading of voltmeter V0 corresponding to full-scale reading I0 of our
constructed ammeter, we need to send a current Im through the voltmeter and the
remaining Ish through the shunt. Therefore the shunt resistance Rsh , the maximum
resistance that can allow minimum Ish current, is calculated as,
Ish = I0 − Im =⇒ Rsh =
Ish
V0
Ish
Rsh
converted
ammeter
Im
Rm
i/2
R
(2)
I0
R
V
V
Rm
A
E
E
Fig 2. (a) Circuit for determination of voltmeter resistance, (b) circuit for using the
voltmeter as ammeter.
Conversion of ammeter to voltmeter
Converting an ammeter to a voltmeter involves increasing the resistance of the
ammeter. This is done by adding a high resistance in series with the ammeter. Let
the range of the ammeter be 0 – I0 Amp and we convert it to a voltmeter of range 0
– V0 volt.
To calculate the series resistance Rss , we first determine the ammeter resistance
using the circuit Fig 3(a). Let Rm be the internal resistance of the ammeter, then
the current flowing through the circuit is i = E/(R + Rm ), where E is the input
voltage. The voltage drop across R is Vr and the current is ir = Vr /R. Since i = ir ,
the ammeter resistance Rm is obtained as,
Rm =
(E − Vr ) R
Vr
2
(3)
To calculate Rss we note that the voltage drop across the ammeter, showing full
scale reading I0 , is Vm = I0 × Rm . To make ammeter full-scale to read full-scale
voltage V0 , the remaining voltage Vss = V0 − Vm should drop across Rss and from
this consideration we calculate series resistance as,
Vss
Vm
Vss
=
=⇒ Rss = Rm
Rss
Rm
Vm
Rss
converted
voltmeter
Rm
(4)
A
Rm
R
Vss
V
A
R
Vr
E
E
Fig 3. (a) Circuit for determination of ammeter resistance, (b) circuit for using the
ammeter as voltmeter.
Experimental procedure
1. The first step to convert a voltmeter to an ammeter is to determine the resistance
Rm of the voltmeter. Make the circuit connections as shown in Fig 2(a).
2. Keeping R = 0, adjust the supply voltage E so that the voltmeter shows large
readings Vm .
3. Choose suitable R to reduce the voltage recorded in voltmeter to half, Vm /2.
The voltmeter resistance is then Rm = R. You may choose to plot the Rm
against serial numbers and draw an average line through them to obtain the
average Rm .
4. Calculate the shunt resistance Rsh and fabricate the circuit shown in Fig 2(b).
Use a digital ammeter or a multimeter, set to appropriate range, as the standard
ammeter.
5. Changing the supply voltage for a fixed R (chosen such that the maximum
current in the circuit is little above I0 ), record the converted and the standard
ammeter readings Inew and Istandard .
6. Plot the calibration curve Inew - Istandard versus Istandard .
3
7. Begin converting an ammeter to a voltmeter by determining the resistance Rm
of the ammeter. Make the circuit connections as shown in Fig 3(a). The
resistance R in series with the ammeter must be kept at large value to prevent
large current from flowing through the ammeter and damaging it.
8. Change R appropriately and each time measure the voltage drop across it Vr
with a digital voltmeter or a multimeter. Also change the supply voltage E
to change the Vr . Calculate Rm from these set of readings either by direct
averaging or by ploting Rm versus serial number and drawing an average line.
9. Calculate the series resistance Rss and fabricate the circuit as shown in Fig
3(b). Use a digital voltmeter or a multimeter, set to appropriate range, as the
standard voltmeter.
10. Changing the supply voltage for a fixed R (chosen such that the maximum
voltage in the circuit is little above V0 ), record the converted and the standard
voltmeter readings Vnew and Vstandard .
11. Plot the calibration curve Vnew - Vstandard versus Vstandard .
Data recording and Observations
Converting voltmeter . . . . . . volt to ammeter . . . . . . Amp
Full-scale reading of the voltmeter = . . . . . . volt
Number of divisions in the scale = . . . . . .
Value of minimum division of the voltmeter = . . . . . . volt
Full-scale reading of the converted ammeter = . . . . . . Amp
Number of divisions in the scale = . . . . . .
Value of minimum division of the converted ammeter = . . . . . . Amp
Table 1. Measurement of voltmeter resistance Rm
Serial
No.
...
...
...
...
...
Full deflection
Vm volt R Ohm
......
0
......
0
......
0
......
0
......
0
Half deflection
Vm /2 volt R Ohm
......
......
......
......
......
......
......
......
......
......
Calculation of Rsh :
Im = V0 /Rm = . . . . . . Amp
Ish = I0 − Im = . . . . . . Amp
Rsh = V0 /Ish = . . . . . . Ohm
4
Rm
Average
Ohm Rm Ohm
......
......
......
......
......
......
Table 2. Calibration of the converted Ammeter
Converted ammeter
Inew Amp
......
......
......
Standard ammeter
Istandard Amp
......
......
......
Correction
Inew − Istandard Amp
......
......
......
Converting Ammeter . . . . . . Amp to Voltmeter . . . . . . volt
Full-scale reading of the ammeter = . . . . . . Amp
Number of divisions in the scale = . . . . . .
Value of minimum division of the ammeter = . . . . . . Amp
Full-scale reading of the converted voltmeter = . . . . . . volt
Number of divisions in the scale = . . . . . .
Value of minimum division of the converted voltmeter = . . . . . . volt
Table 3. Measurement of ammeter resistance Rm
Serial
No.
...
...
...
...
...
E
volt
......
......
......
......
......
R
Ohm
......
......
......
......
......
Vr
volt
......
......
......
......
......
Rm = (E − Vr )R/Vr
Ohm
......
......
......
......
......
Average
Rm Ohm
......
Calculation of Rss :
Vm = I0 × Rm = . . . . . . volt
Vss = V0 − Vm = . . . . . . volt
Rss = Rm Vss /Vm = . . . . . . Ohm
Table 2. Calibration of the converted Voltmeter
Converted voltmeter
Vnew volt
......
......
......
Standard voltmeter
Vstandard volt
......
......
......
5
Correction
Vnew − Vstandard volt
......
......
......
2. ELECTROMAGNETIC DAMPING OF A COMPOUND
PENDULUM
Objective: To study the Electromagnetic damping of a compound pendulum.
Introduction:
Damping plays an important role in controlling the motion of an object. It is an effect, which
tends to reduce the velocity of a moving object. A number of damping techniques are used in
various moving, oscillating and rotating systems. These techniques include, conventional friction
damping, air friction damping, fluid friction damping and electromagnetic (eddy current)
damping. Electromagnetic damping is one of the most interesting damping techniques, which
uses electromagnetically induced currents to slow down the motion of a moving object without
any physical contact with the moving object.
To understand the phenomenon of electromagnetic damping, we need to know about
electromagnetic induction (discovered by Michael Faraday in 1831) and eddy currents (also
known as Foucault currents - discovered by Leon Foucault in 1851). Electromagnetic induction
is a phenomenon, in which an electromotive force (emf) is induced in a conductor, when it
experiences a changing magnetic field. An emf is induced when either the conductor moves
across a steady magnetic field or when the conductor is placed in a changing magnetic field. Due
to this induced emf and the conducting path available, induced currents (flow of electrons) are
set up in the body of the conductor. These induced currents are in the form of ‘eddy currents’
which are electrons swirling within the body of the conductor like water swirling in a whirlpool
(eddy).
The eddy currents swirl in such a way as to create a magnetic field opposing the change in the
magnetic field experienced by the conductor in accordance with Lenz’s law. Thus the eddy
currents swirl in a plane perpendicular to the magnetic field. These eddy currents interact with
the magnetic field to produce a force, which opposes the motion of the moving conductor or
object. The damping force increases as the distance of the conductor decreases from the magnet.
This damping force is also proportional to the
strength of the magnetic field and the induced
Compound pendulum
eddy currents and hence the velocity of the object.
Thus faster the object moves the stronger is the
damping force. This means
ans that as the object
slows down, the damping force is reduced,
resulting
ng in a smooth stopping motion.
In this experiment, a magnet is attached to a
compound pendulum and a metal sheet is placed
at certain distance from the magnet. The metal
sheet should be placed in such a way that it is
parallel
to
the
plane
of
oscillation
and
perpendicular to the length of the magnet as
Magnet
Copper plate
Mirror
Fig. 1: Experimental set up
shown in Figure 1. While the pendulum oscillates, the magnetic flux passing through the metal
will change and induce eddy current in the metal plate.
Apparatus
Compound pendulum with a pointer,
pointer tripod stand, set of magnets, copper
plate with holder, mirror, graph paper to mark position of pointer, stopwatch.
Theory
l
Consider a compound pendulum pivoted about a horizontal frictionless
axis through P and is displaced from its equilibrium position by an angle
θ (see Fig. 2).. In the equilibrium position the center of gravity G of the
body is vertically below P. The distance GP is L, the mass of the body is
m and I is the moment of inertia of the body through the axis P.
P Then the
equation of motion of for small amplitude oscillation is given by
&θ& Thus the solution of Eq. 1 becomes,
… … (1)
Fig. 2: Compound Pendulum
θ = θ 0 sin (ω 0 t ) …
….
(2)
where θ 0 is the maximum angular amplitude, ω 0 = 2π/ T0 =
mgL
. So time period for free
I
oscillation of the pendulum is given by
T0 = 2π
I
mgL
…
…
(3)
When the oscillation is damped due to any resistance in the path such as friction or eddy current
etc, the damping force exerted at the free end of the rod is directly proportional to velocity, v, of
the free end. Let γ be the constant of proportionality called as damping coefficient, then this
force can be written as
F= -γv = - γlω
…
…
(4)
where l= actual length of the rod, ω= angular velocity and the negative sign indicates that the
force is always directed opposite to the velocity. Then torque is given by
•
l F = −γ l 2ω = − γ l 2 θ
…
…
(5)
Thus the equation of motion for a damped oscillation is given by
I&θ& = − mgLθ − γ l 2θ&
…
…
(6)
…
…
(7)
The solution of this modified equation is
= where τ =
2I
, is called as decay constant and is the angular frequency of damped oscillation.
γ l2
Thus, θ becomes maximum (but < θ0 due to exponential decay function in Eq. 7), for = 2,
where n= 0, 1, 2… If T1is time period of this damped oscillator, then it attains maximum
displacement at times, t=nT1 . Hence the maximum displacement of the pendulum decreases
exponentially with time as given by the following equation:
= …
…
(8)
Equation 8 can be rewritten in terms of an equation of a straight line as follows:
θmax
ln θ0
≈ ln
xn
x0
= - n
τ
…
…
(9)
where x0 is the initial and xn is the final linear amplitude after n oscillations. Knowing τ from the
slope of the straight line, the damping co-efficient can be calculated as
γ=
2 I
…
…
(10)
Procedure
1. The compound pendulum is mounted on a tripod stand with two pin pivot arrangement.
Make sure that the pendulum does not slip from the pivot.
2. Fix the magnet to the pendulum using adhesive tapes.
3. Place a mirror vertically very close to the pin attached to the pendulum as a pointer.
Adjust the position so that the image of the tip of the pin can be seen in the mirror
avoiding parallax error. A graph sheet is pasted on the mirror to mark and note the linear
amplitudes of the pendulum. Mark the equilibrium position on the graph sheet.
4. Place the copper plate at a distance, say about 15 mm, so that the plane of copper plate is
perpendicular to the axis of the magnets (see Fig.1).
5. Measure the time period for 10 oscillations by using a stop watch provided. Repeat it for
3 to 5 times to find the average time period of oscillation.
6. Displace the pendulum from the mean position to a position of initial amplitude, x0 (say
about 20mm), and then leave it to oscillate. Note the final amplitude after 2 oscillations.
Repeat it for at least three times, and then find the average value of x2.
7. Repeat the above step for 4, 6, 8, 10 oscillations keeping the initial position fixed.
8. Fill up the observation table and plot a graph between the number of oscillations, n vs
ln x . Determine the slope using straight line fitting and find decay time τ.
0
9. Finally, calculate the damping co-efficient ‘γ’ using the given values of I and l.
Observations
Given: Moment of inertia of the supplied rod, I = 0.0235 kgm2
Length of the rod, l = 0.61m
Table 1: Time period of damped oscillation
d = ……
Sl.
Time for 10
Time period T1
Average time period T1
No.
Oscillations (sec)
(sec)
(sec)
1
2
3
4
5
Table 2: Measuring Amplitude with damping
x0 = ……. mm
No. of
Sl. No.
(mm)
Oscillations
(n)
2
1
2
3
4
4
5
6
..
xn
xn/x0
ln (xn/x0)
Graph:
Plot n vs ln
x0
Slope = …..
Calculations:
τ = ……
γ = …..
Estimation of error:
Precautions:
1. Avoid parallax error while noting the amplitude.
2. Mark the amplitude carefully on the graph sheet pasted on the mirror without disturbing
the set up.
Horizontal component of Earth’s magnetic field ( ) using a Tangent
Galvanometer
AIM: To determine the horizontal component ( ) of the earth’s field.
APPARATUS: (1) Graduated Compass (2) Current carrying coil (3) Rheostat (4) power supply
(5) switch for changing direction of current (6) Ammeter(Digital Multimeter) (7) spirit level
THEORY:
The horizontal component of earth's magnetic field, BH, is the projection of earth's magnetic field
on surface of the earth. Earth’s magnetic field varies with longitude and latitude. Horizontal
component of earth’s magnetic field (BH) in Bhubaneswar is 39 uT. To know magnetic field on a
given location visit this link. http://www.ngdc.noaa.gov/geomag-web/#igrfwmm
Tangent law
Consider a bar magnet with magnetic moment M, suspended horizontally in a region where there
are two perpendicular horizontal magnetic fields, and external field B and the horizontal
component of the earth’s field BH. If no external magnetic field B is present, the bar magnet will
align with BH. Due to the field B, the magnet experiences a torque , called the deflecting
torque, which tends to deflect it from its original orientation parallel to BH. If θ is the angle
between the bar magnet and BH, the magnitude of the deflecting torque will be,
The bar magnet experiences a torque due to the field BH which tends to restore it to its original
orientation parallel to BH. This torque is known as the restoring torque, and it has magnitude.
The suspended magnet is in equilibrium when,
Rearranging gives ------(1)
The above relation, called the tangent law, gives the equilibrium orientation of a magnet
suspended in a region with two mutually perpendicular fields.
Tangent Galvanometer:
A tangent galvanometer works based on Tangent law. It consists of a number of turns of copper
wire wound on a hoop. At the center of the hoop a compass is mounted. When a direct current
flows through the wires, a magnetic field is induced in the space surrounding the loops of wire.
This magnetic flux is designated by Bi. The strength of the magnetic field induced by the current
at the center of the loops of wire is given by Amperes law:
Induced
. --------(2)
where µ0 is the permeability of free space and has the value of 4x 10-7 Newton/Amp2, N is the number of
turns of wire, ‘i’ is the current through the wire, and R is the radius of the loop.
When the wire loops of the tangent galvanometer are aligned with the magnetic field direction of
the Earth, and a current is sent through the wire loops, then the compass needle will align with the vector
sum of the field of the Earth and the induced field as shown in Figure 1.
Magnetic
North
Bresultant
B of Earth
Compass Needle
Direction
θ
Bi
(induced)
Fig. 1
Rheostat
A
Reversing
Switch
Fig. 2: CIRCUIT DIAGRAM
Tangent
Galvanometer
The horizontal component of the magnetic field of the Earth (BH) is calculated from the
following relation:
--------------(3)
Diameter of the coil (R) = 13.6 cm.
Procedure:
1. Level the graduated compass by a spirit level and also see that the current carrying coil is
vertically placed.
2. Set the compass needle to 0-0 position. If there is offset in the pointer in the needle note
down the value.
3. Connect the power supply, rheostat, ammeter and reversing switch as per the circuit
diagram.
4. Connect the current carrying coil from the reversing switch to 50 turns position.
5. Always set the rheostat in middle position.
6. Slowly vary the power supply to set current in the ammeter (connect the digital
multimeter in mA range with DC mode).
7. Note down the deflection in the compass for both left and right direction.
8. Always try to take observations in the range of 15°-75° in the compass.
9. Turn the power supply to initial position, then reverse the current direction at the
reversing switch and repeat the measurements (use same current values).
10. After completing for 50 turns, follow the same procedure for the 500 turns position of the
coil.
11. Compare the obtained magnetic field with Horizontal component of magnetic field at
Bhubaneswar.
Table 1: For 50 turns
Current
(mA)
Deflection of compass
Left
Right
Deflection of compass Bi (Tesla)
by reversing current
direction
Left
Right
BH (Tesla)
Deflection of compass Bi (Tesla)
by reversing current
direction
Left
Right
BH (Tesla)
Table 2: For 500 turns
Current
(mA)
Deflection of compass
Left
Results:
Right
Magnetic field variation along the axis of a circular coil and a Helmholtz coil
Aim: 1) To study the variation of magnetic field along the axis of a circular coil
2) To study the principle of superimposition of magnetic field using a Helmholtz coil
Apparatus:
Constant current Power supply DC 0-16 V, 5 Amp, Digital Gauss meter with Axial Hall Probe
(Transducer), Current carrying coil with 390 turns (N), Diameter 150 mm, support base and
stand, Deflection compass, multimeter and connecting leads
Theory: The intensity of magnetic field at a point ‘P’, lying on the axis of a circular coil ‘AB’
or radius ‘a’ having ‘n’ turns at a distance ‘x’ from the centre ‘O’ of the coil in S.I. units, is given
by
2
· 4 ⁄
Where I is the current flowing through the coil, µ 0 is the permeability of free space, which is
equal to 4π·10-7 H/m.
Fig. 1
The direction of the magnetic intensity at P is along OP if the current flows through the coil in
the anti-clock-wise direction as seen from P. If the direction of the current is clockwise the field
at P is along PO.
The value of the magnetic intensity is maximum at the centre of the coil and is given by
2
·
4
1
Fig.2
If we move away from O towards the right or left, the intensity of the magnetic field
decreases. A graph showing the relation between the intensity of the magnetic field B and the
distance x is given in Fig.2. The curve is first concave (towards O) but the curvature becomes
less and less, quickly changes sign at P and Q and afterwards becomes convex towards O. It can
be shown that the points of inflexion P or Q where the curvature changes its sing lie at distances
‘a/2’ from the centre. Hence the distance between P and Q id equal to the radius of the coil.
A pair of current carrying coils connected in series and separated by radius of the coils is
known as Helmholtz coil. Helmholtz coil produces a uniform magnetic field between the coils,
which is given by
v 8µ NI
B= o
xˆ
125 R
Procedure
i.
ii.
iii.
Using spirit level verify and adjust that track for moving the Hall probe is horizontal and
track is at the centre of the current carrying coils.
Connect the DC supply, Ammeter (Multimeter in current mode), first circular coil in
series as shown in the figure 3. Get the circuit checked by T.A. before switching on
the power supply.
Adjust zero knob such that magnetic feild is zero at the centre of the coil without
switching on the power supply.
2
iv.
Switch ‘ON’ the DC supply. Rotate the current knob to 1/3 rd of full movement and then
increase the voltage. Check the current. Increase the voltage till current is 0.5 Amp. If
needed, rotate current know slightly to get 0.5 Amp.
v.
Note that current should be constant throughout the experiment. Check it before
taking each reading in the multimeter.
You are provided with an axial Hall probe connected to a Gauss meter. End portion of
the probe detects magnetic field. Move it to centre of the coil and check the position at
which magnetic field is maximum.
Place the given compass on the track and find the direction of magnetic field. Then
determine the current direction in your coil (clock wise/Anticlock wise)
Remove the compass from the track and move the Hall sensor to 10 cm left of the left
coil.
Take readings of magnetic field for each 0.5 cm from 10 cm left to 10 cm right of the
coil and tabulate. Magnetic field in Gauss meter fluctuates due to electronics used. At
each step, wait for few seconds and note down the average value.
Switch off the supply and place the second coil at a distance equal to radius of the coil.
Disconnect the first coil and make connections to second coil and repeat the
measurement as above.
Third measurement is for Helmholtz coil setup. Make connections as in Figure 2. Check
with compass that magnetic field is in same direction for both the coils.
Measure magnetic field from 10 cm left of the first coil to 10 cm right of the second coil
for each 0.5 cm.
vi.
vii.
viii.
ix.
x.
xi.
xii.
xiii.
xiv.
Draw the graphs between distance and magnetic field due to COIL 1, COIL 2 and
BOTH along the axis of coils in a single graph and estimate the radius of the coil.
xv.
Calculate the radius of coil to verify with the given value
xvi.
where B is field of the coil the centre of the coil.
v 8µ NI
Calculate magnetic field at the centre of the Helmholtz coil using B = o
xˆ
125 R
3
A
Coil 1
0-16 V DC
Fig. 3: Experimental Arrangement for single coil
A
Coil 1
0-16 V DC
Fig.4: Experimental Arrangement for Helmholtz coil
4
Coil 2
Observations
Sensor
position
(cm)
COIL 1 field COIL-2
(Gauss)
(Gauss)
field Both coils field
(Gauss)
Helmholtz
arrangement
Precautions
1) Care should be taken that there is no stray magnetic field or ferromagnetic material,
such as keys, screwdriver etc. near the setup, while performing the experiment.
2) The radius of the coil is calculated from the centre of winding and not from the
inside edge of the coil bobbin.
3) The Zero of the Gauss meter should be adjusted each time before beginning the
experiments and verified after the completion of experiment by reducing the current
in both the COILS to zero.
Questions: 1) What is a solenoid? What is the variation of magnetic field along the axis of
solenoid?
5
Resolving Power of a telescope with a rectangular aperture
Objective:
•
To determine the resolving power of a telescope with a rectangular aperture
Apparatus:
Telescope, variable rectangular slit, Na lamp, source slits
Theoretical background:
A simple telescope consists of a large aperture objective lens with high focal length and
an eye piece with a lower focal length and smaller aperture. An eye piece consists of two lenses
separated a distance. The lens towards the objective is called the field lens and other which is
near to the eye is known as eye lens.
The resolving power of an optical instrument, say a telescope or microscope, is its ability
to produce separate images of two closely spaced objects/ sources. The plane waves from each
source after passing through an aperture from diffraction pattern characteristics of the aperture. It
is the overlapping of diffraction patterns formed by two sources sets a theoretical upper limit to
the resolving power.
Consider two narrow slit sources, d distance apart, kept at a distance D away from the
aperture, i.e. objective, of a telescope. In the following we will stick to rectangular aperture.
Then the angular separation α of the slits at the aperture is α = d/D. Each slit will produce its own
single slit diffraction pattern, for which the intensity distribution is given by,
, where (1)
And is the slit width, θ is the angle of diffraction and λ is the wave length of light from the
sources. The principal maximum of each slit corresponds to θ = 0 0 and the position of
the minima, which are points of zero intensity, corresponds to , 2 etc. The angular
separation of the two principal maxima is equal to the angular separation of the sources, i.e. α.
The Rayleigh’s criterion for resolution of two diffraction patterns states that two sources
or their diffraction patterns are resolved when the principal maximum of one falls exactly on the
first minimum of the other. Since the first minimum is formed at , then angular separation
α of the maxima is equal to the corresponding θ1,
sin (2)
The angle is known as minimum angle of resolution while 1" is sometimes called the
resolving power of the aperture . For circular aperture, Rayleigh’s criterion is modified to
1.22 $" . To find the intensity at the centre of the resultant minimum for the overlapping
diffraction fringes separated by , we note the curves of principal maxima cross at "2for
either pattern. Therefore intensity at the centre, relative to the maximum, is sum of the intensity
of either at "2,
%& '
%(
2 )
*
0.8106
(3)
Procedure:
1. Make the axis of the telescope horizontal by adjusting it with a spirit level and its height is to
be adjusted that the images of the pair of slits are symmetrical with respect to the cross point of
the cross wires.
2. The images are brought into sharp focus by adjusting the telescope while keeping the variable
aperture wide open.
3. Reduce the width of the aperture gradually so that at first the two images appear out and
ultimately their separation vanishes. Measure the width of the aperture at this critical position.
Reducing aperture further and
note the reading when the illumination (light) just disappears altogether. The difference of these
two readings gives width of the aperture required.
4. Now begin with a closed aperture gradually increasing the width. Take the first reading when
the illumination just appears and then when the two images just appear to be separated. The
difference giving the width of the aperture is noted.
5. Repeat the operation 3 and 4 for three or four times.
6. Measure the distance between the slits (sources) and the objective of the telescope by means
of measuring tape.
7. Observe that as you increase the distance D between the telescope aperture and source for a
fixed d and λ, you need larger aperture to resolve the two sources. It is needless to mention that
larger aperture implies larger light gathering capacity.
For fun, you can test how good the resolving power of your eyes are by looking at the second
star from the tip of the handle of Big Dipper or saptarshi mandal in the constellation of Ursa
major. The name of the bright star is Mizar
(vasistha), but it has a faint optical companion called Alcor (Arundhati) and the ability to resolve
the two stars with naked eye is often quoted as a test of eyesight.
8. Observe the construction of telescope. What are the components used in the telescope? Pull
out the eye piece and observe the location of cross wires. Which type of eye piece is used in the
telescope? Ramsden’s or Huyghen’s? What is the difference between these two types of
eyepieces?
Fig. 1 Experimental setup
Observations
Determination of least count of the traveling microscope
Value of smallest main scale division (MSD) = ……………………………
…………………….vernier scale division = ………………………..main scale division
Hence, 1 vernier scale division = …………………………main scale division (VSD)
Vernier Constant (VC) = (1 – VSD) x MSD = …………………………….m
Table-I. Determination of the source slits separation d
Mean d
Mean T
d (m)
T = M + VC x V
Vernier (V)
Main scale (M)
Mean T
Right slit
T = M + VC x V
obs
1
Vernier (V)
Slit edge
Main scale (M)
Left slit
- =
L
2
- - ~ /
3
………
1
/ =
R
2
/ / ~ -
3
Least count of screw gauge attached to the aperture
Value of smallest main scale division (MSD) = ……………………………
Number of circular scale division (CD) = …………………………………….
Screw Pitch (P) = 1/CD = ……………………Least Count (LC) = P x MSD = ………....m
Table II. Determination of minimum angle of resolution θ1 at varying D
Wavelength of light used λ = 589.3 x 10-9m. Average source slits separation d = ……….m
0
1
Obs D (m)
1a
1b
1c
.
.
.
6a
6b
6c
.
.
.
.
.
.
Open
slit Closed slit Number of circular scale circular scale rotated
2 ) 34
(C0)
(C1)
division
&5'
N)
$
(radian)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Plot the 6 graph, explain why it gets difficult to achieve increasingly low ?
Questions
1. How the minimum angle of resolution changes with the wavelength of the light $?
2. Which one of the two telescopes, optical and radio has more resolving power for a given
aperture?
3. What is the for human eye for red (700nm), yellow (600nm), and blue (400nm) light,
assuming dark-adapted average pupil size is 5mm? (Use the Rayleigh’s criterion for
circular aperture.)
Dispersion of light by a prism
Aim: (i) To calculate refractive index µ of a prism for various wavelengths (λ) of Hg and to find
dispersive power of the material of the prism.
(ii) To plot µ-1/λ2 curve and hence determine Cauchy’s constants for the prism material.
Apparatus: Spectrometer, prism, Hg lamp and spirit level
Theoretical background
When a ray of light is refracted by a prism, the angle between the incident and refracted ray is
called the angle of deviation δ. For a given prism angle A and wavelength λ, δ depends on the
angles of incidence i and emergence r (See Fig. 1). The angle of deviation is minimum when the
angles of incidence i and emergence r make equal angles with prism surfaces, i.e. i= r. We
denote this angle of minimum deviation as δm which depends on the wavelength of the light used.
Refractive index of the prism for a given wavelength of light λ is related to the corresponding δm
by,
(1)
If µ 1 and µ 2 are refractive indices of the material
of the prism for wavelengths λ1 and λ2, and µ is
the refractive index of λ, which is the mean of λ1
and λ2, then dispersive power is defined as
(2)
Fig. 1
Using Eq.(1), µ(λ) of the prism can be obtained experimentally by determining δm for the
corresponding λ. Thus a calibration curve of µ-λ can be drawn for the prism from which the
refractive index can be determined for a given wavelength or vice-versa. The experimental µ-λ
curve can be described with a fair degree of accuracy by the empirical Cauchy’s equation,
,
(3)
where C and D are Cauchy’s constants for the prism material. The plot µ versus 1/λ2 is a straight
line from which C and D values can be determined by fitting the data with Cauchy’s relation.
The dispersion of the material of the prism is defined as ⁄, which can be obtained from the
Cauchy’s formula in eqn. (2),
!
"
,
(4)
1
Experimental set up:
In this experiment, we will use a prism spectrometer to measure the deviations of light for
various wavelengths. The detail description of the spectrometer is already provided as a separate
note. Before starting the experiment please identify all parts of the spectrometer. Familiarize
yourself with
ith the focusing adjustments and also coarse and fine movement of different parts.
Fig. 2: Experimental set up
Procedure:
1. DO NOT PLACE THE PRISM ON THE SPECTROMETER YET.
2. First check leveling of the spectrometer base, prism table, collimator and telescope.
telescope If
needed, level them using the adjustment screws and a spirit level.
3. The collimator is adjusted for parallel beam of light and the telescope for focusing the
parallel beam by Schuster’s method (details of which is given iin
n another experiment). But the
present set up may not require it.
4. Adjusting the telescope: While looking through the telescope, slide the eyepiece in and out
until the crosswire comes into sharp focus. Point the telescope at some distant object and
view it through the telescope. Turn the focus knob of telescope until the image is sharp. The
telescope is now focused for parallel light rays. DO NOT change the focus of the telescope
henceforth.
5. Ensure the Hg lamp is fully illuminated and placed close to the sl
slit
it of the collimator. Check
that the slit is partially open.
6. Adjusting the collimator: Align the telescope directly opposite the collimator and look
through the telescope, to see a focused image of the slit. If necessary, adjust the slit width
2
until the image of the slit as seen through the telescope is sharply focused on the crosswire.
The collimator is then set to produce parallel light from the slit.
7. Determine the vernier constant of the spectrometer. Report all the angles in degree unit.
Details about reading angles in spectrometer are given in the manual for finding angle of
minimum deviation.
8. Angle of prism: (Refer Fig. 2)
• Place the prism such that its vertex is at the center
of the prism table, directly in line with the
illuminated slit.
• The opaque face (AC) should face towards you so
that light from the collimator is reflected at the
two faces AB and AC.
Telescope
Telescope
• Rotate and adjust the telescope to position I where Position-II
Position-I
the image of the slit reflected at AB is centered on
the crosswire. Record the angular positions on
each vernier.
• Now, turn the telescope to position II for the
image reflected at AC and record again the
angular positions on each vernier.
• Take three independent sets of readings for
Fig. 2
telescope position I and II on each vernier. Let the
mean of these three sets of readings of the two
verniers V1 and V2 are respectively,
telescope position I: α1 , α2
telescope position II: β1 , β2
• Then the mean angle of the prism A is obtained using
#$ $% $# /#, where ' ( ~* and '! (! ~*! .
9. Direct ray reading: Remove the prism from the
spectrometer and align the telescope so that the direct
image of the slit is seen through the telescope centered
on the crosswire. Record the angular position of the
telescope on the two verniers as D1 and D2. This will be
the reference angular position for any measurements
later.
10. Angle of minimum deviation: (Refer Fig. 3)
• Replace the prism on the spectrometer table so that it is
oriented as shown in Fig. 3.
• Locate the image of the spectrum with naked eye. Then
rotate the telescope to bring the spectrum in the field of
view.
• Gently turn the prism table back and forth. As you do so,
the spectrum should appear to migrate in one direction
until a point at which it reverses its direction.
• Lock the prism table. Now, using fine adjustment screw
Fig. 3
3
of the telescope fix the crosswire on one of the spectral lines of wavelength λ1 at an extreme
end.
• Then move the prism table using fine adjustment screw so that the angle where the line starts
reversing its direction is precisely located. Take three such independent readings. Let the
mean of these readings on the two verniers V1 and V2 for λ1 are θ1 and θ'1. Calculate the mean
value of δm(λ1) as follows:
1
δmλ 0θ ~D θ3 ~D! 4
2
• Similarly, note down the angles of minimum deviation for all the spectral lines, whose
wavelengths and colors are given in the chart. (see last page)
11. Calculate the refractive index for each wavelength using Eq.1 and then determine the
dispersive power using Eq. 2.
12. Plot µ ~ (1/ λ2) and determine Cauchy’s constants by least square fitting.
OBSERVATIONS
Table 1: Determination of vernier constant (VC) of the spectrometer
Value of 1 small main scale division (MSD) = ………
……. vernier scale divisions = ….. main scale divisions
Hence, 1 vernier scale division = ………… main scale division (VSD)
Vernier Constant (VC) = (1 – VSD) x MSD = ………
Table-2. Determination of the angle of the prism
1
2
3
1
V2
2
(
=
(!
=
3
4
2A (degree)
Mean 2A
(degree)
Mean T
(degree)
T = M + (VC
x V)
Vernier (V)
Reflection image 2
T = M + VC
xV
Mean T
(degree)
Main scale
(M)
Vernier
V1
Reflection image1
Main scale
(M)
Vernier (V)
obs
* '
( ~ *
*! '!
(! ~ *!
2'
' '! 5
2
A
(degree)
Table-2. Direct ray reading
Vernier
Obs.
Main scale (M) Vernier (V)
T = M + (VC x V)
Mean (degree)
1
2
3
1
V2
2
3
Table-3. Angle of minimum deviation for various λ
6
V1
Color
/ λ(
nm)
Color
.
.
.
Vernier
Obs
V1
1
2
3
1
2
3
.
.
.
V2
.
.
.
V1
Color
9
V2
Main
Scale(M)
Vernier
(V)
6!
T = M + (VC
x V)
Mean
(degree)
δm(λn)
(degree)
θ
θ ~D
θ3
θ3 ~D!
Mean δm(λn)
(degree)
78 ……………
.
.
.
.
θ
1
2
3
1
2
3
θ3
θ ~D
θ3 ~D!
78 9 ……………
Table-4. Determination of refractive indices :; and data for : < %/;# plot
angle of the prism, A = ….
Color
(nm)
1/! (nm-2)
78 ..
..
..
..
..
..
………..
………..
.
.
.
.
………..
………..
.
.
.
.
………..
………..
.
.
.
.
………..
………..
.
.
.
5
Calculations:
Dispersive power of prism =
Cauchy’s constants: Using least square fitting in < 1/! plot
C = …..
D = ……
Precautions:
1. Do not touch the refracting surfaces by hand. Place the prism on the prism table or remove it
from the prism table by holding it with fingers at the top and bottom faces. The reflecting
surfaces of the prism should be cleaned with a piece of cloth soaked in alcohol.
2. Rotate the adjustment screws slowly. Do not force any movement. If something is not
moving check the clamping screw. Use fine adjustment screw after locking the clamping
screw.
Questions: 1) What is normal and anomalous dispersion? Where do you get anomalous
dispersion?
2) What are the factors on which the dispersive power of a prism depends?
Additional Reading:
1. Feynman lectures on physics, volume 1. Narosa Publishing House, Delhi
2. Practical Physics, R.K. Shukla and A. Srivastava, New Age International (P) Ltd.
6
Newton’s rings
Apparatus:
Traveling microscope, sodium vapour lamp, plano-convex lens, plane glass plate, magnifying
lens.
Purpose of the experiment:
To observe Newton rings formed by the interface of produced by a thin air film and determine
the radius of curvature of a plano-convex lens.
Basic Methodology:
A thin wedge shaped air film is created by placing a plano-convex lens on a flat glass plate. A
monochromatic beam of light is made to fall at almost normal incidence on the arrangement.
Ring like interference fringes are observed in the reflected light. The diameters of the rings are
measured.
I. Introduction:
I.1 The phenomenon of Newton’s rings is an illustration of the interference of light waves
reflected from the opposite surfaces of a thin film of variable thickness. The two interfering
beams, derived from a monochromatic source satisfy the coherence condition for interference.
Ring shaped fringes are produced by the air film existing between a convex surface of a long
focus plano-convex lens and a plane of glass plate.
I.2. Basic Theory:
When a plano-convex lens (L) of long focal length is placed on a plane glass plate (G) , a thin
film of air I enclosed between the lower surface of the lens and upper surface of the glass
plate.(see fig 1). The thickness of the air film is very small at the point of contact and gradually
increases from the center outwards. The fringes produced are concentric circles. With
monochromatic light, bright and dark circular fringes are produced in the air film. When viewed
with the white light, the fringes are coloured.
A horizontal beam of light falls on the glass plate B at an angle of 450. The plate B
reflects a part of incident light towards the air film enclosed by the lens L and plate G. The
reflected beam (see fig 1) from the air film is viewed with a microscope. Interference takes place
and dark and bright circular fringes are produced. This is due to the interference between the
light reflected at the lower surface of the lens and the upper surface of the plate G.
1
For the normal incidence the optical path difference between the two waves is nearly 2µt,
where µ is the refractive index of the film and t is the thickness of the air film. Here an extra
phase difference π occurs for the ray which got reflected from upper surface of the plate G
because the incident beam in this reflection goes from a rarer medium to a denser medium. Thus
the conditions for constructive and destructive interference are (using µ = 1 for air)
2 t = m λ for minima; m =0,1,2,3… … … … … .. -----(1)
and 2 t = (m+1/2λ) for maxima; m = 0,1,2,3… … … … … . -------------(2)
Then the air film enclosed between the spherical surface of R and a plane surface glass plate,
gives circular rings such that (see fig 2)
Fig. 2
Fig. 3
2
If Dm is the diameter of the mth bright ring from the centre then
2 1
(3)
Where R is the radius of curvature of the plano convex lens, λ is wave length of light. Equation 3
can be written as
22 1
(4)
II. Setup and Procedure:
1. Clean the plate G and lens L thoroughly and put the lens over the plate with the curved surface
below B making angle with G(see fig 1).
2. Switch in the monochromatic light source. This sends a parallel beam of light.
3. Look down vertically from above the lens and see whether the center is well illuminated. On
looking through the microscope, a spot with rings around it can be seen on properly focusing the
microscope.
4. Once good rings are in focus, rotate the eyepiece such that out of the two perpendicular cross
wires, one has its length parallel to the direction of travel of the microscope. Let this cross wire
also passes through the center of the ring system.
5. Now move the microscope to focus on a ring (say, the 20th order dark ring). On one side of
the center. Set the crosswire tangential to one ring as shown in fig 3.
Note down the microscope reading (Make sure that you correctly read the least count of the
vernier in mm units)
6. Move the microscope to make the crosswire tangential to the next ring nearer to the center and
note the reading. Continue with this purpose till you pass through the center. Take readings for
an equal number of rings on the both sides of the center.
Now move the microscope to focus on a ring (say, the 20th order dark ring). On one side of the
center. Set the crosswire tangential to one ring as shown in fig 3. Note down the microscope
reading.
(Make sure that you correctly read the least count of the vernier in mm units)
3
6. Move the microscope to make the crosswire tangential to the next ring nearer to the center and
note the reading. Continue with this purpose till you pass through the center. Take readings for
an equal number of rings on the both sides of the center.
7. Use Equation 4 to find the Radius ‘R’ of plano convex lens by least square fitting. Wave
length of sodium light (λ) is 5893 Angstrom.
Table: Measurement of the diameter of the rings
Ring
No. (m)
Microscope reading
Left reading (R1)
Diameter
Dm=R1~R2
(cm)
Right reading (R2)
Dm2
2(2m+1)
1
2
3
..
..
..
..
Precautions:
Notice that as you go away from the central dark spot the fringe width decreases. In order to
minimize the errors in measurement of the diameter of the rings the following precautions should
be taken:
i) The microscope should be parallel to the edge of the glass plate.
ii) If you place the cross wire tangential to the outer side of a perpendicular ring on one side of
the central spot then the cross wire should be placed tangential to the inner side of the same ring
on the other side of the central spot.(See fig 3)
iii) The traveling microscope should move only in one direction to avoid backlash error.
Reference: Practical Physics by R.K. Shukla and A. Srivatsava, New Age International Ltd.
4
Laser Diffraction and Interference
Objective
• To determine the wavelength of laser light from a thin wire diffraction pattern.
• Compare the thickness of the wire with the single-slit width that form the same diffraction
pattern as wire and hence verify the Babinet’s principle.
• To explore the double-slit interference pattern.
Apparatus
Laser source (and safety goggles), screen & ruled-paper for recording, thin-wire source, variable
single-slit and double-slit sources, grating, measuring tape, travelling microscope and (if
available) digital camera
Theoretical background
When light passes through a small opening or around an edge, secondary waves from different
portions of the emerging wavefront will, in general, travel different distances before reaching a
screen. Although the waves from secondary sources are all in phase to start with, they will be
out of phase by the time they reach the screen. The interference of these radiation emitted by
secondary on the wavefront leads to the phenomenon of diffraction. We will study only
Fraunhofer diffraction, where the light source, screen and the object causing diffraction are
effectively at infinite distances from each other.
Single-slit diffraction
When a light of wavelength λ is incident normally on a narrow slit of width b, the resultant
intensity of the transmitted light is given by,
, with (1)
where, θ being the angle of diffraction. The diffraction pattern consists of a principal maximum
for β = 0, where all the secondary wavelets arrive in phase, and several secondary maxima of
diminishing intensity with equally spaced points of zero intensity at β = mπ. The positions of
the minima of a single-slit diffraction pattern are,
mλ = b sin θ, m = ±1, ±2, ±3, . . . .
sin ,
m = ±1,±2,±3…….. (2)
1
If θ is small i.e. the slit to screen distance D is large compared to the distance xmbetween two
m-th order minima (on either side of principal maximum), then
sin ……(3)
The above equation (3) can be used to determine the wavelength of the monochromatic light
source, laser in present case, by measuring b, D and xm for various m. The positions of the
minima can be obtained by averaging the two extremities of the zero intensity region, as shown
in the picture below.
Figure 1. Single-slit diffraction pattern – distance between minima xm is calculated from the
average minima position on either side of principal maxima.
Diffraction of a thin wire
If the single-slit is replaced by a thin wire obstacle, which blocks as much laser light as a
single-slit will allow to pass, the resulting diffraction pattern will be identical to that of a singleslit. Knowing the wavelength λ of the laser light, the equation (3) can be used to determine the
thickness of the wire b as,
(4)
A typical diffraction pattern of a wire obstacle is shown below. Here too, the positions of the
minima are calculated by averaging the two ends of the spread of zero intensity regions as shown
in Fig 2.
Figure 2. Diffraction pattern from wire obstacle– similarity with single-slit pattern is what
Babinet’s principle asserts. xm is measured as in single-slit case.
2
The fact that Fraunhofer diffraction pattern due to an obstacle is virtually identical to that of an
opening of same dimension is an example of a general rule called Babinet’s principle. This
principle can be verified by replacing once again the wire with a single- slit and varying the slitwidth until the pattern matches exactly. The slit width can then be compared with the wire
thickness.
Dobule-slit interference
If instead of single-slit, we have two parallel slits each of width b separated by an opaque space
of width c, the corresponding intensity distribution of the Fraunhofer pattern formed is,
cos
(5)
Where being the angle of diffraction,
,
! ,
d= b + c,
(6)
The intensity distribution is a product of two terms: the first term (sin2 β/β2) represents
diffraction pattern produced by single-slit (eqn.1) and the second term cos2 γ is the characteristic
of interference produced by two beams of equal intensity and phase difference γ. The overall
pattern, therefore, consists of single-slit diffraction fringes each broken into narrow maxima and
minima of interference fringes. This interference of light from two narrow slits close together
was first demonstrated by Thomas Young in 1801 and helped establish the wave nature of light.
The minima for the interference fringes are at γ = (2p + 1)π/2 with p = 0, 1, 2, . . . and those for
diffraction fringes are at β = mπ where m = 1, 2, 3, . . .. The conditions for minima are,
&
" sin #$ % ' sin (7)
(8)
A typical double-slit Fraunhofer pattern obtained with laser beam is shown in Fig 3. The
intensity of laser may render viewing the pattern difficult without photographing.
Figure 3.
Double-slit interference pattern – each diffraction maxima is broken up into
interference fringes. The minima positions xp (interference) and xm (diffraction) are read off
directly without averaging.
3
Procedure
WARNING: The laser beam can cause real damage to your eyes if you look into the beam
either directly or by reflection from shiny objects.
1. Determine the vernier constant of the travelling microscope and measure the thickness b of
the wire, slit-width b for single and double slit, and slit plus opaque space d = b + c of
double-slit.
2. Arrange the screen at least 2 meter away from the laser source. On the screen, attach a ruledpaper with clips such that the ruled scale is horizontal. You may use graph paper in place of
ruled-paper, if you consider it convenient.
3. Turn the laser on and be extremely careful not to let your eyes in the direct or reflected line of
the laser. Does not turn the laser off and on too frequently; instead use something to block the
laser when it is not in use.
4. Adjust the height of the laser (and also the screen) such that the laser spot is directly on the
ruled line in the middle of the paper.
5. To record the pattern that will be produced on the screen, mark the fringe pattern with pencil
on edges of bright spots on both left and right side of the central maximum. Calculate the
midpoints of minima and subtract one from other to find fringe width ( )* ~),
6. First place a thin wire apparatus close in front of the laser and observe the diffraction pattern
on the screen. Adjust the laser and slit so as to obtain a bright, crisp pattern. Measure the slit to
the screen distance D with a measuring tape. Calculate the wavelength of the laser in use from
the data and equation (3) by straight line fit.
7. Next replace the wire with a single slit and adjust the width of the slit to match the pattern
which was obtained with the wire. Keep the distance between slit and screen same as in the wire
screen distance. Calculate the thickness of the single slit using traveling microscope and compare
the result to the value wire thickness to verify Babinet’s principle.
8. To explore the double-slit pattern, proceed exactly the same way as single-slit, but this time
around it may be difficult to mark off the diffraction minima directly on the screen although the
interference minima are fairly easy to spot. Show the pattern to instructor. You do not need to
take any observations for this part. What type of patterns you expect with multiple slits?
4
Observations and results
Value of smallest main scale division (MSD) = . . . . . .
. . . . . . vernier scale division = . . . . . . main scale division
Hence, 1 vernier scale division = . . . . . . main scale division (VSD)
Vernier constant (VC) = (1 − VSD) × MSD = . . . . . .
Table I. Determination of wire thickness
Wire
αl=
αr=
5
αl ~αr
Mean b (m)
b (m)
Mean T
T = M + VCxV
Vernier (V)
Main Scale (M)
Right edge
Mean T
T = M + VCxV
Vernier (V)
Obs
1
2
3
Main Scale (M)
Object
Left edge
Table-II. Determination of wavelength of the laser light
Wire thickness =…….
Ord
er
Slit screen distance D=……
Left fringes
Left
edge
(cm)
Right
edge
(cm)
Right fringes
Average,
)*
(cm)
Left
edge
(cm)
Right
edge
(cm)
Fringe
width
Average,
),
(cm)
(
)* ~),
(cm)
1
2
3
.
.
.
Plot Xm versus m and by straight line fitting find slope and determine wave length (λ).
Table III. Determination of the single-slit width to prove Babinet’s principle
Single
slit
el =
6
er=
el ~ er
Mean b (m)
b (m)
Mean T
T = M + VCxV
Vernier (V)
Main Scale (M)
Right edge
Mean T
T = M + VCxV
Vernier (V)
Obs
1
2
3
Main Scale (M)
Object
Left edge
Questions:
1.
In what way interference and diffraction differ?
2. What would you expect if ordinary sodium lamp (supposing it to be monochromatic) is
used instead of laser? What if white light is used?
3. Why the positions for minima are measured instead of maxima in the cases of single-slit,
wire and double-slit pattern? [Hint: the maxima are not in the center of the bright
region.]
4. What is missing order? Do you expect to get one in the present experimental setup?
7
STUDY OF POLARISATION AND MALUS’S LAW
AIM: To study Polarization of light and verification of Malus’s law.
APPARATUS: Laser (diode/He-Ne), Optical profile bench, analyzer (polarising filter) photo
detector, and digital multimeter attached to an amplifier, mounts for all above components.
THEORY:
Let AA′ be the Polarization planes of the analyzer in the figure given below. If the linearly
polarized light, the vibrating plane of which forms an angle φ with the polarization plane
impinges on the analyzer, only the part
EA=E0cosφ
-- (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 on (Malus’ law) is obtained.
IA= I0. cos2φ -- (2)
A
φ
EA
E0
EA=E0cosφ
A’
PROCEDURE:
1. Laser should be warmed up for about 15-30 minutes to prevent intensity of fluctuations.
2. Make sure that the photo detector/photocell is totally illuminated when the polarization
filter is set up.
3. The background voltage V0 must be determined with the laser switched off and this must
be subtracted from actual readings.
4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90°
and note down corresponding photo cell voltage V.
5. Plot (V-V0) Vs φ and determine the angle of polarization of the given laser(θ).
6. Plot cos2 (φ-θ) Vs (V-V0)/(Vmax-V0) and fit the straight line to find slope and verify
Malus’s law.
TABULATION:
V0=__________V
Table 1
Sl.
No.
1
2
..
..
Angular Position of analyzer
in degrees
Photo cell voltage(V)
in volts
V-V0
in volts
Angle of polarization of the laser θ = __________
Table 2
Sl. No.
1
2
..
..
cos2 (φ-θ)
(V-V0)/(Vmax-V0)
PRECAUTIONS:
1. Never look directly into the laser beam.
2. Photocell readings should be taken carefully.
3. Do not change the direction of the laser as it may affect other experiments in the room.
You are allowed only slight adjustment of the direction.