Diffraction and Interference of Light
Physics 100L Exercise 9
Particle or Wave?
The underlying nature of light has long been a major subject of controversy
among scientists. Newton advocated the notion that light beams were
comprised of particles, and developed a rather complete theory of optics
(the study of light) based on this idea. Robert Hooke, a Newton
contemporary and fierce adversary, had a competing theory that treated
light as a wave phenomenon.
Light – particle or wave?
In 1860, James Maxwell, building on the works of Oersted and Faraday that we have seen in the
previous two labs, developed a complete theory of electromagnetism. When he solved his
equations, he found solutions that corresponded to waves of electric and magnetic fields (dubbed
the “electromagnetic field”) that propagated through space at the speed of light. It was only a
small step to conclude that these solutions in fact represented light waves, and he found that
these waves had very high frequencies, between 4  1014 and 8  1014 Hz. Maxwell achieved the
physicists dream – in one brilliant stroke of genius, he united the previously separate theories of
electricity, magnetism, and optics.
Physicists at this period time thought the debate was settled. After all, Maxwell’s theory
provided not only theoretical elegance, but experimental confirmation as well. It led to the
discovery of other forms of “light” such as x-rays and radio waves. In the early 1900’s,
however, Einstein and Planck once again revived the debate when they showed that previously
unexplainable phenomena could be simply explained if one treated light as a stream of particles.
These were only the beginnings of what turned out to be a major revolution in physics, the
quantum mechanics. Today physicists regard light as both particle and wave, and depending on
what experiment you are doing light will either behave more like a wave or more like a particle.
In fact, it was found that even things that had always been thought of as particles, such as
electrons and protons, also behaved like waves under certain circumstances. Truth is indeed
stranger than fiction.
Interference
In today’s experiment, we will examine two of the
phenomena that lent credence to the wave theory of light
when they were discovered during the last century. The
Constructive interference
first of these is known as interference – when two waves
are in the same region of space, they interfere with each
other. We discussed an example of this when we talked
about sound waves and beats. The idea is that if there are,
Destructive interference
for example, two waves, then the resulting wave is the sum
of those two waves, where you add the waves point by
point. If the two waves are in phase, i.e., when the crests of one coincide with the other, the
result is that the waves increase each other, and this is called constructive interference. When
the two waves are out of phase, i.e. the crests of one wave coincide with the troughs of another,
the result is that the waves tend to cancel each other out, and this is called destructive
interference. These two effects are illustrated in the diagrams at right. Needless to say,
interference is a wave-only phenomenon. Particles cannot interfere with each other.
Two-slit Interference
The wave nature of light can be clearly demonstrated by the interference of light waves emerging
from two nearby slits. View the pattern that you see on a screen that is illuminated by a laser
beam passing through a two-slit aperture. You should see rather broad bright and dark regions
on the screen. If you look closely, you will see, superimposed on this pattern, a series of more
closely spaced bright and dark bands. The broad pattern is the diffraction pattern, which we will
discuss shortly, but the more finely spaced bands are the interference pattern produced by the
two slits. The centers of the bright bands correspond to regions where the distance that the light
wave from one slit travels is an integer number of wavelengths different from that traveled by the
light wave from the second slit. That being the case, the waves arrive at the screen in phase, and
thus a bright band is seen. The centers of the dark bands correspond to regions where the path
length difference for the two waves corresponds to an integer number of wavelengths plus an
extra half wavelength. In this case, the waves from each slit arrive at the screen out of phase,
and hence a dark band results.
If you know the distance between the two slits, the positions of the bands on the screen can be
used to determine the wavelength of the light. According to Pythagoras, the distance dleft
traveled by a wave from the left slit to a point P on the screen is approximately given by
d left  L2  ( x  2 ) 2
where L is the distance from the slits to the screen, x is the distance along the screen from the
middle of the central band to the point P, and  is the distance between the slits. For this
equation to be correct, we must be measuring at a point P to the left of the center. The distance
traveled by a wave from the right slit is slightly longer:
d right  L2  ( x  2 ) 2
Measure the distance from the slits to the screen L, and for x use the distance from the middle of
the central stripe to the middle of the tenth bright stripe to the left of the center. The distance  is
indicated on the slit holder. Using these values, calculate dleft and dright, and find the difference
between the two (don’t round off the numbers). How is this difference related to the wavelength
of light? Use your results to determine the wavelength of the laser light.
Diffraction
The other phenomenon that we will examine briefly is known as diffraction, and, like
interference, it is a wave-only phenomenon. Examine what appears on the screen when a laser
beam passing through a single adjustable slit illuminates it. When the slit is very narrow, there is
a broad region of light on the screen. To each side of the region there are bright and dark bands.
This is called a diffraction pattern. A detailed discussion of diffraction is beyond the scope of
this course, as it requires a great deal of mathematics. What is happening is that the light from
the slit is interfering with itself, and this produces the pattern, which can be predicted and
understood very well using integral calculus. Adjust the slit width and see what happens to the
pattern. Make a rough plot of central band width vs. slit width – is it what you expect?