PHY 1033C
Lab #4
September 21, 2010
Measurement of Wavelengths of Light
Goal: Measure the wavelength of light with a diffraction grating.
Introduction:
A transmission diffraction grating consists of a thin piece of clear plastic which contains many
closely-spaced scratched parallel lines, from which light scatters as if from many parallel slits.
When a beam of light is incident on a diffraction grating, part of the light passes straight through the
grating (in the direction of the incident light) and part of the light is diffracted by the grating into
different propagation directions. The scratches are very narrow (less than a wavelength) and each
re-radiates the light incident on it in all directions; the fraction of the incident light propagating in a
given direction is the sum of the light emitted in that direction by the many line slits, like a sum of a
number of 2-slit interference patterns.
Just like the 2-slit case,
the rays emitted by the
individual slits at the
angle θ (see Fig. 1) will
all be focused by the
lens at its focal point F.
But if the light arriving
at the grating from the
left is in phase, then the
light reaching F will in
general not be in phase,
since each ray travels a
different distance from
Figure 1
the particular scratch to
the focal point of the
lens. The rays will interfere constructively or destructively and the actual intensity of the light
striking F depends upon the path differences. If the difference in path length traveled by adjacent
rays is a whole number of wavelengths all of the rays will be in phase and will add constructively to
produce a bright spot of light at F. The difference between two adjacent paths is the segment AB
in Fig. 1, whose size is related to the scratch spacing d and the deflection angle θ by
AB = d sinθ
Maximum light intensity will be produced at F if AB is an integral number of wavelengths:
d sinθ = mλ
The value of m is called the order of the diffracted beam. In general, the intensity of the diffracted
beam decreases as the order increases. Since sinθ cannot exceed unity the order m cannot exceed
d/λ. If the beam of light incident upon the grating contains a number of wavelengths (i.e. colors),
each wavelength will have its own angle of deviation in each order. This results in a complete
spectrum of the source for each diffraction order.
Procedure:
In this experiment the grating is placed close to your eye and the eye lens serves to collect the light.
Make the distance L between the diffraction grating and the source S 1 meter and place a small
piece of masking tape to mark the spot. Place the meterstick at the base of the source S (the light) so
that the 50 cm mark is located at S. Looking through the diffraction grating located 1 m from S you
will see diffracted images (bands) of color on both sides of the undiffracted image. A different set
of images will be present for each color in the incident light. For a given color (red, green, or blue)
there will be two images on opposite sides and at equal distances D from the filament in the light
(see Fig. 2). While one person looks through the grating he/she should direct a second person to
move a finger along the meterstick until his/her finger reaches the middle of each band of color.
Measure the distance D for the middle of each band of color (Red, Blue, Green) on both sides of the
source, and average to get he
best value.
Measurements of D and L will
give tanθ from which sinθ and
λ may be computed. Although
both first and second order
images may be visible, we will
not study the second order ones.
Note: your grating is scratched
13,400/inch and 1 inch = 2.54
cm. Draw a picture of the
set-up (Fig. 2) in your lab
notebook. Construct a table of
Figure 2
your
measurements
and
calculate the average wavelength for each color as a result. Show your calculations. Make a “ruler”
of color vs. wavelength (color with smallest wavelength first). Compare your results to the table
below:
Table of Wavelengths for Light emitted from “Hot” Atoms
Mercury
Color
Wavelength (x10-10 m)
Yellow
5791
Yellow
5770
Green
5461
Blue-Green(Weak)
4916
Blue-Violet
4358
Violet(Weak)
4078
Violet
4047
Color
Red
Red
Yellow
Green
Blue-Green
Blue
Blue-Violet
Helium
Wavelength (x10-10 m)
7065
6678
5876
5047
4922
4713
4471