Experiment 3: Interference and Diffraction
Part I: Interference and Diffraction of Water Waves.
The apparatus is a ripple tank, as used in PHY 131. A glass-bottomed tank of water is between a
light above and a screen below. Waves in the water act as lenses, each projecting a bright area onto
the screen, so the wave pattern can easily be viewed.
A) Flat waves from a vibrating wooden bar pass through an opening in a barrier in the tank. You
will observe how the amount of diffraction through this opening depends on wavelength.
(Diffraction is the bending of waves around an obstacle.)
Start up the ripple tank and build a wall out of paraffin blocks
across it, with an opening about 2 cm wide. The two balls on
the ripple bar should be turned up out of the way. Vary the
wavelength and the size of the opening to compare the
behavior of waves whose wavelength is larger than the
opening to waves which are a good deal smaller than the
opening. Sketch what you see.
As your conclusion for this part, state under what conditions
waves more or less reach all places behind the wall, and under
what conditions they don't.
B) The bar is raised above the water, and two plastic balls hung from it now each send out circular
ripples. These two coherent sources are equivalent to double slit interference... You will check on
whether the double slit equation, mλ = d sinθ, is obeyed by separately determining mλ and d sinθ
from measurements of the pattern.
Turn the two balls down and adjust the bar supports so
that the bar is out of the water and the balls are about
half submerged. Get a picture showing several areas
of constructive and destructive interference. Cover the
screen with paper by taping several sheets together and
draw a straight line up the center of each beam (area of
constructive interference) through second order. Do
not try to trace the beams too close to the sources; mλ
= d sinθ is not valid at small distances. Please do not
mark the screen itself. With a ruler, extend the first
order lines until they meet, and measure the angle formed. Divide by 2 to get θ measured from the
center. Repeat for second order; these lines may not cross at the same point that first order did.
Notice that there is a standing wave along the line between the two sources, formed by the identical
waves traveling in opposite directions. This is the easiest place to measure the wavelength. (Each
flickering bright spot is an antinode. For best accuracy, measure across a number of them and
divide. Think carefully - many people overlook a factor or two.) Also measure d, the distance
- 2 between the two sources. Measured d on the screen, not at the balls themselves, to be consistent
with your other measurements.
Separately calculate mλ and d sinθ for the first two orders. For your conclusion, say whether the
equation mλ = d sinθ seems to be correct. (Assume 10% uncertainty in both mλ and d sinθ.)
Part II: Diffraction grating.
Caution: Looking directly into the laser beam is dangerous like looking at the sun. Keep the beam
and its reflections down at table-top level and keep your eyes above this level.
You will check whether light passing through a grating obeys the grating equation. (You have a
round piece of clear plastic with thousands of evenly spaced scratches on it, too small to see. The
way light scatters from these scratches is equivalent to having many parallel slits. As we will see in
section 4, multiple slits produce interference maxima at the same angles that two slits do; they are
just narrower maxima. So, the grating equation is the same as the equation for the maxima of a
double slit pattern.)
Mount the grating in the beam from the laser, it and locate the first order maxima on the wall
beyond. They're at a fairly large angle. If you have trouble finding them, place a sheet of paper a
few inches from the grating, where you can find them easily, then follow them out. Ignore any
spots only a degree or two from the central maximum. These
are due to periodic spacing errors on the grating. Measure the
distance from the central maximum to the first order on each
side, and average. (They may not be the same if the grating and
screen are not parallel. Averaging corrects for this.) Note that
the end of the tape measure is as shown.
Find θ from the geometry of the situation. (Not from mλ = d sinθ. mλ = d sinθ is what you're trying
to verify - using it as part of its own proof is circular reasoning.) Find d from the fact that there are
5300 lines per centimeter. Then, calculate the quantity d sinθ (assume it is 3% uncertain). In your
conclusion, compare this to mλ. The wavelength of a helium-neon laser is 632.8 nm.
Part III. Thin film interference.
You will use interference of light to measure the thickness of a piece of plastic, and compare the
result to what you get with a micrometer.
The thin film in this case is made of air, sandwiched
between a pair of glass plates. Rubber bands clamp
the plates in contact at one end, while a thin piece of
plastic holds their other ends apart, making the air
- 3 space wedge shaped. This is viewed with monochromatic light from a mercury lamp, which is
reflected from both the top and bottom of the air gap. Where the plates touch, the path difference
between these rays is zero, and they interfere destructively there. (One of them undergoes a phase
reversal on reflection.) A little over from there, where the gap is λ/4, the path difference is λ/2,
giving constructive interference. Where the gap is λ/2, it’s back to destructive interference, and so
on. Along the glass, you will see alternating bands of bright and dark, one dark band to the next
being an increase of λ/2 in the gap. Thus, counting how many dark bands there are from the contact
point to the edge of the plastic tells you the thickness of the plastic in terms of the light’s
wavelength.
Please do not take the apparatus apart, as the glass will then probably have to be cleaned before the
experiment will work again.
Observe interference fringes by looking at the reflection of the mercury lamp. With its green filter,
this lamp radiates light with a single wavelength, 546 nm. Count (as accurately as you can) the dark
interference fringes along the length of the air wedge. Moving some sharp pointer, such as a pencil,
along the glass will help you keep track of where you are as you count. You will have to move the
lamp to see them. Use this number to compute the thickness of the plastic.
Use a micrometer to measure its thickness directly. Enough plastic hangs out the side for you to do
this without taking things apart. First, check how the micrometer is zeroed. You will probably find
that it's off by at least a fraction of a division. Then, when you read the thickness of the plastic,
correct your reading accordingly. Estimate an uncertainty for both values of the thickness.
In your conclusion,
1. State whether they agree with each other, and also
2. Comment on which method is the most accurate and why.
All together, this lab asks for five conclusions: One each for parts IA, IB, II, and the two questions
just above for III.
- 4 Phy 133
Experiment 3: Interference and Diffraction
Part I:
A)
Finish Pictures:
B) Two Source Interference:
λ = __________________
First Order:
d = __________________
Second Order:
= __________________
= __________________
mλ = __________________
m λ = __________________
d sin
= __________________
d sin
= __________________
Part II:
A) y = _________________
Calculate θ:
dist. to screen = ________________
- 5 d sinθ = ______________
mλ = __________________
Part III:
Number of fringes =
Compute thickness:
Measured thickness =