PHYSICS EXPERIMENTS — 132
16-1
Experiment 16
Diffraction and Interference of Light
Laser light can damage the retina.
Keep the laser level at all times to avoid shining
the light into an eye either directly or off of a
reflecting surface.
WARNING:
In this experiment you observe the patterns
formed by laser light after passing through different
types of openings. The patterns, observed far
behind the openings, consist of definite distinct
areas of light and dark. The spatial variations in
light energy arise from the constructive and
destructive interference of light waves. The spatial
distribution of energy in an interference pattern
allows precise determination of the size and shape
of the opening the light passes through, essentially
allowing very precise distance measurements in
terms of numbers of light wavelengths.
known, the diffraction pattern may be used to
determine the wavelength of the light. Screens used
for this purpose are called diffraction gratings.
Diffraction gratings consist of many narrow, evenly
spaced slits. The many slits increase the amount of
destructive interference, so that the constructive
interference regions are very distinct and their
positions easy to precisely measure. The change in
the diffraction pattern as more slits are used is
shown in Figure 1.
2 slits
3 slits
Preliminaries.
Light is an electromagnetic wave. It has the
wave properties of amplitude, frequency,
wavelength, and speed. As with any wave, the
Principle of Superposition describes the treatment
of multiple light waves overlapping in space. If the
light waves overlap in phase, differing by an integer
number of complete wavelengths, constructive
interference results and bright areas appear. If the
light waves overlap out of phase, differing by an
odd integer number of half wavelengths,
destructive interference results and dark areas
appear.
There are many ways to get light waves to
overlap in space. The most basic is to send a single
light wave through an opaque screen with
transparent slits in it. Each slit in the screen
becomes a wave source. Waves from the slits
overlap in the region behind the screen, where a
distinct diffraction pattern of interference maxima
(bright, constructive interference) and minima
(dark, destructive interference) appears.
The distribution of light in a diffraction pattern
depends on the wavelength of the light as well as
the features of the screen (width of slits, distance
between slits, number of slits, etc.). When light
travels through a screen whose features are well
7 slits
Figure 1. Diffraction patterns for different numbers
of slits.
Usually the distance between the lines in a
diffraction grating is specified by its reciprocal, the
line density . This value is usually expressed in
units like 1/mm.
The use of diffraction patterns to determine
wavelengths of light sources is known as
spectroscopy. This is an extremely important
diagnostic tool for identifying materials, as the
distribution of wavelengths is distinctive and acts
like a fingerprint.
If the wavelength(s) of the light source is well
known, the diffraction pattern may be used to
determine the features of the screen. Here, the light
is being used as a ruler, with the wavelength being
the ruler divisions. The wavelength of visible light
is roughly tenths of micrometers (10-7m), so that
measurements of length by diffraction analysis are
roughly one thousand times more precise than those
using an ordinary meter stick.
The light sources used in this experiment are
lasers. Lasers produce narrow beams of light at,
16-2
PHYSICS EXPERIMENTS — 132
essentially, a single wavelength. This simplifies the
diffraction pattern analysis.
Figure 1 shows that the locations of the
interference maxima are independent of the number
of slits in the diffracting screen (although the width
of the maxima does change). The maxima locations
are positions of constructive interference where
light waves from adjacent slits arrive at the viewing
screen an integer number of wavelengths apart, as
shown in Figure 2.
central part of the diffraction pattern, characterized
by angular position < 150, the small angle
approximation   tan  sin  where  is
expressed in radians can be used to a precision of
two significant figures. In this case, the interference
maxima are evenly spaced at a distance y given by

y=R/d
The discussion above is concerned with light
waves originating from different slits. Light coming
through a single slit can also show interference.
This is because each point on the slit can be thought
of as a wave source. The light passing straight
through the slit will produce a bright central
maximum. The first minimum on either side of this
central maximum will occur when the light from the
upper half of the slit interferes destructively with the
light from the lower half. This condition is:
a sin  =
Figure 2. Constructive Interference between
Adjacent Slits
When light of wavelength  travels through a
diffraction grating (or a double-slit) with slit
spacing d, the interference pattern has maxima
(bright spots) at angular position m given by
dsin( m )  m
(eq. 1)
where m = 0, 1, 2, 3 is the order number.
Some
 basic trigonometry applied to Figure 2
shows that a feature in the interference/diffraction
pattern at angular position  appears on a viewing
screen at distance y from the center of the pattern
given by
y  R tan 
(eq.2)
where R is the distance from the slide to the viewing
screen. When eq. 1 and eq. 2 are applied to the

(eq.3)


(eq.4)
where a is the slit width,  is the wavelength, and 
is the angular position of the minimum as indicated
in Figure 3. on the next page. This Figure shows
that, for every ray leaving the upper half of the slit,
there is a corresponding ray from the lower half
which will be  out of phase when the two rays
combine at the first minimum position. If rays 1
and 2 are out of phase by 2 then rays 2 and 3 will
also be out of phase by , or (a/2) sin  = /2. The
pairs of rays will therefore interfere destructively to
produce a minimum.
PHYSICS EXPERIMENTS — 132
16-3
• Measure and record the distance R from the
grating to the viewing screen.
• Measure the distance y1 from the center dot to
the one immediately next to it on the left. Measure
the distance from the center dot to the one
immediately next to it on the right. These distances
should be the same. If they are not, take the average
and record it.
• Calculate the line spacing d for the grating from
the line density.
• Calculate the wavelength  of the laser using eq.
1 and eq. 2.
Figure 3. Diffraction through a Single Slit
Note: Eq. 1 and eq. 4 are identical in
form but refer to quite different
physical situations. Eq. 1 identifies
interference maxima for multiple slits,
while eq. 4 identifies an interference
minimum for a single slit.
In this experiment a spectroscopic analysis of
laser light using a grating is performed to determine
the wavelength of the laser. Subsequently, the
known wavelength of the laser is used in a
diffraction pattern analysis to determine slit widths
and slit spacings.
Procedure.
Part A. Diffraction Grating
• Pass the laser beam through the diffraction
grating. Make sure that the beam is perpendicular
to the grating and to the viewing screen.
• Move the grating closer to the viewing screen.
Observe the effect of the change in distance on the
pattern on the viewing screen. Return the grating to
its original position.
• Find the manufacturer specified line density  of
the grating. Record the value.
Part B. Single Slit
• Shine the laser through the single slit. Make sure
that the beam is perpendicular to the viewing screen
and to the slide containing the slit.
• Measure and record the distance R from the slit
to the viewing screen.
• Record the distance 2y1 from minimum to
minimum on either side of the central maximum.
Turn off the lights to make sure find the minima.
• Calculate the slit width a. Use the standard
value of = 632.8 nm for the red laser wavelength.
Part C. Double Slit
• Shine the laser through the more closely spaced
double slit. Make sure that the beam is
perpendicular to the viewing screen and to the slide
containing the slits.
• Measure and record the distance R from the slits
to the viewing screen.
• Record the distance y between maxima around
the center of the pattern. Think about the best way
to do this in view of the discussion above eq. 3.
Turn off the lights to make sure find the maxima
and minima.
• Calculate the slit spacing d. Use the standard
value of = 632.8 nm for the red laser wavelength.
16-4
Questions (Answer clearly and completely).
1. At the position of the maximum corresponding
to m=4 in eq. 1, how much further has the light ray
from one of the slits traveled compared to the light
ray from the slit next to it? from the light ray two
slits away? Consider Figure 2 carefully.
2. How does the pattern change as the distance
between the grating and viewing screen changes?
What does this indicate about how light energy exits
the grating?
3. What value do you determine experimentally in
Part A for the wavelength of the laser light? The red
laser wavelength is very well known to be = 632.8
nm. Determine the percent difference of the
experimental value from the standard value.
4. In Part B, you are asked to measure from
minimum to minimum rather than from center to
minimum? Why? Is this a good idea?
5. What value do you determine experimentally for
the width of the slit?
6. The “ideal” double slit diffraction pattern
consists of interference maxima which are all
equally bright.
Is this what you observe?
Describe/sketch carefully what you do observe.
Explain why you see what you do see? [Suggestion:
look at the single slit pattern again.]
7. What value do you determine experimentally for
the distance between the centers of the slits in the
double slit?
PHYSICS EXPERIMENTS — 132