PHY 1033C
Lab #4
September 27, 2011
Measurement of Wavelengths of Light
Goal: Measure the wave length of light with a diffraction grating.
Reference: Ch. 4 in text
Introduction
A transmission diffraction grating consists of a thin piece of clear plastic on which are scratched
many closely-spaced 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 rulings.
The rays emitted by the
individual slits at the
angle θ (see Fig. 1) will
Diffraction Grating
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
the particular scratch to
the focal point of the
Lens
lens. The rays will
interfere constructively
or destructively and the
Figure 1
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 wave lengths 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, 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 wave lengths:
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 wave length 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.
An aperture through which light from the source may pass is mounted in front of the source S.
Measure the distance L between the diffraction grating and the source S. Looking through the
grating you will see diffracted images of the aperture on both sides of the un-diffracted 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
aperture (see Fig. 2)
Measurements of D and
L will give tanθ from
which sinθ and λ may be
computed (see lecture 7
and Ch. 4 in text).
Although both first and
second order images will
be visible, we will not
study the second order ones.
Note: your grating has a
scratch spacing d =
13,400/inch and 1 inch =
2.54 cm.
Figure 2
Draw a picture of the set-up (Fig. 2) in your lab notebook. Construct a table of your measurements
and results. 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