Download Prism Spectrometer

Spectrometer
Prism Spectrometer
-1-
Spectrometer
Table of Contents
Section Page
Back ground ........................................................................................................ 3
Basic Experiments
Experiment 1: Prism spectrometer ........................................................... 6
-2-
Spectrometer
Back ground
reflection and refraction :
the law of reflection states that for a light ray travelling in air and incident on a
smooth surface , the angle of reflection
equals the angle of incidence :
light crossing a boundary as it travels from medium 1 (with light speed
medium 2 (with light speed
) to
) is refracted or bent . the angle of refraction
is
defined by the relationship :
From this equation we can infer that when light moves from a material in which its
speed is high to a material in which its speed is lower ,the ray is bent toward the
normal and vice versa.
index of refraction :
the index of refraction is a property of a medium and defined by
where is the speed of light in vacuum and
is the speed of light in the medium .In
general , varies with wavelength and is given by
where
is the vacuum wavelength and
is the wavelength in the medium .note that
as light travels from one medium to another it s frequency remains the same .
snell's law of refraction states that:
Where
and
are the indices of refraction for the two media.The incident ray ,the
reflected ray ,the refracted ray and the normal to the surface all
lie in the same plane.
Dispersion:
Dispersion is the phenomenon which gives you the separation
of colors in a prism.
For a given material, the index of refraction varies with the
wavelength of the light passing through the material.
-3-
Fig.1
Spectrometer
The relation between the refractive index and wavelength of light for a particular
transparent material is given by Cauchy's equation :
where A and B are material-dependent constants. Note that the larger the value of B,
the more dispersive the medium.
A table of coefficients for common optical materials is shown below:
Glass
A
B (μm2)
BK7
1.5170
0.00422
dense flint
1.5961
0.00880
hard crown
1.5043
0.00455
Table.1
Because
is a function of wavelength, light of different wavelengths is bent at
different angles when incident on a refracting material. the index of refraction
generally decreases with increasing wavelength (for visible light). This means that
violet light bends more than red light does when passing into a refracting material.
white light can be separated by a dispersive medium like a prism. Even more effective
separation can be achieved with a diffraction grating.
the separation of colors by a prism we see the continuous range of spectral colors (the
visible spectrum). A spectral color is composed of a single wavelength and can be
correlated with wavelength as shown in the chart below
This progression from right to left is from long wavelength to short wavelength, and
from low frequency to high frequency light.
-4-
Spectrometer
Prism :
A refracting prism is a convenient geometry to illustrate dispersion.
Prisms are typically characterized by their angle of minimum deviation
.
When a ray of single wavelength light incident on a prism from the left
it emerges refracted from its original direction of travel by an angle ,
called the angle of deviation
The minimum deviation angle
Figure.2
can be achieved by adjusting the incident ray
perpendicular to one of the prism's sides which leads that the ray passing through the prism
to be parallel to the bottom of the prism.
And the incident angle =the refracting angle
Using the geometry in the figure, we find that
Where
is the apex angle of the prism .
From snell's law of refraction, with
because.
Figure.3
medium 1 is air
Hence .knowing the apex angle of the prism and measuring
the angle of minimum deviation we can calculate the index of
refraction of the prism material.
-5-
Spectrometer
Experiment 1: Prism spectrometer
Spectrometer:
A spectrometer is an optical instrument for producing and analyzing spectra.
The importance of the spectrometer as a scientific instrument is based on a simple but
crucial fact. Light is emitted or absorbed when an electron changes its orbit within
an individual atom. Because of this, the spectrometer is a powerful tool for
investigating the structure of atoms. It's also a powerful tool for determining which
atoms are present in a substance. Chemists use it to determine the constituents of
molecules, and astronomers use it to determine the constituents of stars that are
millions of light years away.
a spectrometer consists of three basic components As shown in
Figure 4; a collimator, a diffracting element(prism or diffraction grating) , and a
telescope.
The light to be analyzed enters the collimator through a narrow slit positioned at the
focal point of the collimator lens. The light leaving the collimator is therefore a thin,
parallel beam, which ensures that all the light from the slit strikes the diffracting
element at the same angle of incidence. This is necessary if a sharp image is to be
formed.
The diffracting element bends the beam of light. If the beam is composed of many
different colors, each color is diffracted to a different angle.
The telescope can be rotated to collect the diffracted light at very precisely measured
angles. With the telescope focused at infinity and positioned at an angle to collect the
light of a particular color, a precise image of the collimator slit can be seen.
Figure 4 Spectrometer diagram
Equipment
-6-
Spectrometer
–Spectrometer :which consists of
a)Collimator and Telescope
collimator is fitted with a 6 mm long slit of adjustable width. The telescope has an
eyepiece with a glass, cross-hair.
b)Rotating Bases
The telescope and the spectrometer table are mounted on independently rotating
bases. Vernier scales provide measurements of the relative positions of these bases to
within one minute of arc. The rotation of each base is controlled with a lock-screw
and fine adjust knob. With the lock-screw released, the base is easily rotated by hand.
With the lock-screw tight, the fine adjust knob can be used for more precise
positioning.
c)Spectrometer Table
The spectrometer table is fixed to its rotating base with a thumbscrew, so table height
is adjustable. Three leveling screws on the underside of the table are used to adjust
the optical alignment. Thumbscrews are used to attach the prism clamp and the
grating mount to the table, and reference lines are etched in the table for easy
alignment.
–Equilateral glass prism.
–Spectrum tube power supply.
–Spectrum tubes such as Mercury, Helium, Cadmium, etc.
–magnifier.
Figure 5 Spectrometer with working parts. Not shown is the vernier window on
the opposite side
-7-
Spectrometer
OBJECTIVE
1) Learn the theory of the prism spectrometer, and explain the functions of its various
components.
2) Measure the apex angle of the prism .
2) Observe the spectrum of the discharge lamp and record the angle of minimum
deviation for the spectral lines.
3) Determine the index of refraction of a glass prism for various colors and to
examine how the index of refraction of the material of a prism depends on the
wavelength of light.
4) Calculate the dispersive power for each color in the spectrum using the Cauchy
equation.
5)Determine the Cauchy constants from the plot and what type of glass constitutes the
prism.
6) Calculate the dispersive power of the prism .
PROCEDURE
1. Turn on the mercury light. It takes a while to warm up.
To save time and frustration, the spectrometers are adjusted through Step 10. Take the
following steps only if instructed to do so by your TA.
Focus Adjustment
2. With no prism on the prism table, focus the telescope at infinity (something at one
end of the room or through the window, not through the collimator). You may have
to loosen the telescope rotation lock screw to freely move the telescope.
3. While looking through the telescope, slide the eyepiece in and out until the cross
hairs come into sharp focus. Do not use the focusing knob to do this. There is a
locking adjustment around the eyepiece that you can loosen. When you tighten it
up again, make sure the cross hairs are aligned so that one is totally horizontal and
the other is vertical. (If it’s rotated a little, it’s hard to align the spectral lines.)
4. If necessary, repeat steps 2 & 3 until the distant object and the cross hairs can be
put in sharp focus at the same time.
5. Check to see that the collimator slit is partially open. Adjust, if necessary.
6. View the collimator slit through the telescope. Focus the collimator (not the
telescope) until the slit comes into sharp focus.
7. Lock the telescope rotation lock screw. Use the telescope rotation fine adjustment
to align the vertical cross hair with the fixed edge of the slit. (The fine adjust does
not work unless the rotation lock screw is set.)
-8-
Spectrometer
Zeroing the Reference Angle
8. Loosen the table base lock screw and rotate the table so that the right window
vernier reads about 0°. Retighten the lock screw.
9. Using the magnifier and the table base fine adjust, set the vernier to read 0° 0'. This is
your reference angle.( Notice that there are two windows in which
you can read an angle. We want to rotate the table until one of the windows has 0
(zero), we should try to use set it so that this window is to the left of the telescope (as
we are looking over the barrel toward the lamp) because this will make reading our
angle easiest.
Setting this to zero means that the vernier reading for a particular spectral line is directly
the angle of minimum deviation. Do not move the table after you have set this angle.
Prism Mounting
10. Mount the prism at the center of the prism table. If necessary, loosen the (long)
table lock screw which fastens the prism table to the base and adjust the height so
that light from the collimator is striking the prism, then lightly tighten the screw.
Recall that the prism orientation for the minimum deviation is where one of the
sides is roughly perpendicular to the incident light beam(the refracted light is
parallel to one of the sides of the prism), as in Fig. 3. The frosted side of the prism
should be to the right as you’re facing the light source.
Measuring the Apex angle
11.Place the prism on the turntable with its frosted side
hard against the lamp and rotate the table until the beam
from the collimator is roughly bisected by the apex of the
prism as in figure 6.The beam will be reflected off both sides
of the prism (each acting like a plane mirror) so two images of
the slit can be observed, one on each side of the prism. The angle
between the two telescope positions is twice the angle of the
prism.
Minimum Deviation Adjustment
Figure.6
12. Set up the spectrometer to view light from the
mercury lamp. (See Fig. 7) Based on Fig. 3, estimate
the direction the dispersed light from the collimator
will exit the prism. With your bare eye, look at the
prism along this direction to find the image of the
collimator's slit. You should see a series of brightlycolored lines.
Note:
measurements should always be made
with the cross hairs aligned on the fixed edge of the
collimator slit. This enables you to adjust the slit's
-9-
Figure.7
Spectrometer
width for optimal line visibility at any time during data collection. This way, your
angle measurement is independent of the width of the slit.
13. If the prism is in exactly the right orientation to provide the angle of minimum
deviation, the series of colored lines move to the right as a whole, whether you
rotate the table clockwise or counterclockwise. rotate the table until you are
satisfied that the orientation is where the lines bounce, or change direction.
14. Now view the lines through the telescope.
a. Rotate the prism back and forth slightly to fine-tune the exact orientation that
puts the lines at their extreme position (the telescope's cross hairs make a
convenient reference mark).
b. Since the position of the prism for minimum deviation is a slowly varying
function of the wavelength, it is not necessary to reset the minimum deviation
for each line (color). Once the prism is set, this orientation should not be
changed for the duration of the experiment.
c. Lightly tighten the prism holder.
Measure
Figure.8
15. Measure
for line in the mercury spectrum:
a. Loosen the telescope rotation lock screw and rotate the telescope so that its
cross hairs are near the fixed-edge side of the slit's image.
b. Lightly tighten the telescope rotation lock screw.
c. Use the telescope fine adjust knob to carefully align the cross hairs and the
fixed-edge side of the slit's image.
d. Find the value of
for this color using the vernier scale.
i. Identify the color from (fig.8) and record the wavelength of the line from
(Table 2).
ii. Record the two numbers from the spectrometer that indicate this angle, the
nearest, lowest half-degree and the minute.
Light
Line Color Wavelength
Source
(Å)
Mercury
Red
6907
Yellow
5790
Yellow
5770
Green
5461
Blue-Green
4916
Blue
4358
Violet
4078
Violet
4047
- 10 -
table.2
Spectrometer
Reading the Angle
The angle
between the moveable telescope and the fixed collimator is
determined using the vernier scale as in (Fig. 9) The bottom degree plate is graduated
in units of 0.5° or 30' (30 arc minutes). The top set of numbers, or the vernier scale,
provides a further resolution of 1' and has a range of 30'. Reading this type of vernier
is the same in principle as the one with the calipers . Follow the procedure below:
Figure 9 The half degree-minute
vernier on the spectrometer.
A. Find the Zero. Locate where the zero mark of the vernier scale aligns with the
degree plate.
B. Record the degrees to the nearest, lowest 0.5°. When the zero of the top scale is
between two lines on the degree plate, use the smaller value. (In Fig. 9), the zero
is between the lines 155° and 155° 30'. 155° is the smaller of the two, so you
record the degrees as 155.
C. Record the minutes. Use the magnifying glass to determine the line on the
vernier scale that aligns most closely with any line on the degree plate. (In Fig. 9),
this is 15', so you write down 15 as the minutes.
D. Add this value to the reading recorded above to get the correct measurement
to within 1 minute of arc: that is, 155 ° + 15' = 155 °15'.
Hints:



Opening up the slit allows more light to come through, increasing the intensity and
allowing you to better see the dimmer lines. However, some of the lines are so close to
each other that a wider slit washes out the distinction. In particular, the two yellow lines
of mercury need a very narrow slit in order to distinguish between the two.
Also, repositioning the lamp can increase the brightness.
You can also use the blackout clothing.
- 11 -
Name:
Computer ID:
Date:
Group:
------------------------------------------------------------------------------------------------------------------------------------------
LAB 3: Prism spectrometer
Results
1.
Measure The Apex angle
of the prism.
2.
Record the angle of minimum deviation
The angle of the unrefracted beam:
3.
for each spectral line in the following table.
=
Calculate the refractive index
for each color using the following formula:
Color
4.
Indicate the relation between the wavelength of each color and its corresponding wavelength
by plotting on the -axis and
on the -axis, and show by what equation are they related.
5.
Plot a diagram between
Cauchy constants, where:
A=V.I (vertical intercept)=
B=slope=
on the -axis and
6.
Determine what type of glass constitutes the
prism.
7.
Calculate the dispersive power D for each
on the -axis to find the value of the
Color
color, where:
8.
Calculate the dispersive power of the prism p.
a.
Calculate the intermediate
wavelength
b.
From your graph locate the position of the intermediate wavelength and its
corresponding refractive index.
n
c.
=
Calculate the dispersive power of the prism, where: