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MPTC
Diffraction
Introduction
Diffraction basically means `spreading out’, while interference is a pattern that emerges
when waves collide. You may have already seen a demonstration of interference with light
waves of a certain color passing through 2 slits in the lecture section of the course. In today’s
lab, we will use light waves containing various colors to observe diffraction and interference by
shining onto a large series of slits (apertures) that are separated from one another by a very small
distance comparable to the wavelength of that wave. Such a series of apertures is called a
“diffraction grating”. You will use interference measurements to then calculate the wavelength
and momentum of visible light, quantities that are far too small to measure directly.
Wavefront
crest

trough
Diffraction
Grating
d

n=
N= 2
2
Constructive
interference
N=0
n=
0
N=1
n=
Observation Screen
If we imagine light as similar to a water wave, with wavecrests (wavefronts) that move
perpendicular to themselves, when a wavefront is incident upon the diffraction grating, parts of
the wavefront are removed and each aperture serves as a source for a new wavefront that spreads
out (diffracts). This is illustrated in the plan-view figure above. Since each of these sources is
driven by the initial wave front, all the sources are in phase (meaning they all crest or trough at
the same time when leaving their aperture). However, by the time the waves collide at some
point on an observation screen behind the grating, they may be out of phase with one another. If
all the peaks or all the troughs of the waves are still synchronized in time there, we say that at
that point there is “constructive interference.” We see a bright region. If, on the other hand, the
peaks of waves from some apertures are synchronized with the troughs of the other waves,
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everything cancels out and we say that “destructive interference” occurred at that point. We see a
dark region on the screen.
If on the other hand we imagine light as a stream of photon particles, we interpret the
intensity of waves at any given place as telling us the probability of detecting a photon there. So
photons are more likely to hit regions on the observation screen that are bright (that is why they
are bright!). We can understand the diffraction process as the uncertainty principle applied to
photons. The grating localizes photon position but introduces uncertainty in the photon
momentum that causes the spreading out.
The dashed directions in the diagram represent the angles of diffraction at which
constructive interference takes place. The “order” N is the way to describe which of the above
directions is involved (N=0, N=1, N=2, …) In this experiment, we will be observing the effect
produced when light from a mercury lamp is passed through a diffraction grating. Such a lamp
produces several colors of light, each of a different wavelength ; each color will have its own
interference pattern with bright regions (spectral lines) of different order N.
Procedure & Equipment
1) Place one meter stick flat on the table with the metric scale up. Have one end of
the stick be flush with the table edge (shown as Observer below) to make
observation easier. Place a second meter stick on edge with the metric scale up,
centered on and perpendicular to the other meter stick as in the diagram. These
meter sticks will be used to measure the angles of diffraction .
Mercury Lamp
Ͽ
grating
y
Caution!
 Take care when handling the lamp – if the bulb breaks, the mercury
vapor inside is highly poisonous.
 Take care when handling the lamp – it uses a very high voltage, don’t
stick your fingers anywhere near the bulb ends.
2) Position the Mercury lamp on end behind the second meter stick as shown; turn it on.
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Caution!
 Don’t touch the actual diffraction grating film – you will damage it.
3) Position the grating (in its holder) perpendicular to and at one end of the 1st meter stick.
4) Your eye is going to be the observation screen. Place your eye on a level with the grating
and look through it, back towards the lamp. Directly ahead, the light source should be
visible; this is the N=0 image. Further to the right (or left) you should see the colors of
violet, green, and yellow with violet closest to the center (diffracted the least). These 3
lines compose the first order diffraction (N = 1). Looking even farther out should reveal
a second similar set of colored lines. This is the second order diffraction (N = 2).
5) Record data in the first four columns of Table 1 for every line you can see.
Trouble Shooting
 You may need to bring your eye closer to the grating
 Move your line of sight, not the grating
 The grating may not be oriented correctly in its holder – take out and rotate by 90 0
 Remove any other light source in your line of sight
Analysis
After you have taken all your data, calculate the angles of diffraction from trigonometry.
The grating has 13400 apertures per inch. Use this calculate the distance d in cm (1 inch = 2.54
cm) between successive apertures.
Hence calculate the wavelengths for each observed spectral line using the diffraction formula
N = d sin 
If you observed different orders of diffraction, calculate the wavelengths of the same color for
the different orders of diffraction.
Use the de Broglie formula p =h / to calculate the momentum of a photon in one of your
spectral lines and compare the value to a typical macroscopic momentum in mechanics.
Consider the position and momentum uncertainty of individual photons in the x direction as they
pass through the grating. Given that one is uncertain about precisely which aperture each photon
goes through, what is the smallest distance uncertainty? Given that the photons were collimated
before going through the grating, how could you estimate the momentum uncertainty introduced
by the grating? Verify that your uncertainties satisfy Heisenberg’s principle.
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Table 1
Color
N
Y
x














Discussion Questions
1. How did  change with angle of diffraction?
2. Was the wavelength of a particular color different for different orders of diffraction?
Should it be?
3. Would contamination (such as the presence of another gas) in the tube affect your
data? If so, how?
4. If we could somehow detect which aperture each photon goes through (reducing
position uncertainty to zero) what should we then see on the observation screen?