Experiment 4
Laser Interference and Diffraction
Preparation
Prepare for this experiment by looking up Huygens' Principle, interference, and single and
double slit diffraction.
Principles
Start with a single slit of width a, placed a distance L from a screen. Consider what happens to
coherent monochromatic light as it passes through the slit. According to Huygens' Principle each
part of the slit will act as a point source sending light out in all directions. When the light from
all the points strikes the wall a distance L from the slit patterns of light and dark spots can be
seen. This is because nearly parallel beams arriving at the wall are superimposed and there is a
difference in the distance traveled by light that passed through different parts of the slit.
The equation for destructive interference for monochromatic light of wavelength λ passing
through a single slit of width a is
asinθ = mλ , where m = 0, ±1, ±2, ...
and m is called the order number.
Figure 1. The light pattern created by passing monochromatic light through a single slit. m or n
are sometimes used to denote order numbers.
Look up single and double slit diffraction on Hyperphysics. There are illustrations of the
patterns created by shining a laser through a single or double slit. The single slit produces a
pattern with a broad central maximum with narrower maxima on either side. If you call the
distance from the center of the central maximum to the first minimum y, you can find sinθ for m
y
= 1 and then find a. Since θ is so small, you can use the approximation sinθ = tan θ = .
L
The distance between the other maxima or minima is not constant, but the differences are
relatively small if the distance between the slit and the screen is large. You can find the average
distance between minima and use it for y.
The equation for constructive interference for a double slit with slit separation d is
dsinθ = mλ , where m = 0, ±1, ±2, ...
In this case, the maxima and minima are nearly the same width. Again, you can find the average
distance between maxima or minima and use that value for y where m = 1.
Figure 2. The pattern created by passing monochromatic light through a double slit.
Equipment
table clamp
threaded rod
90° clamp
short rod
slit holder
slit
lab jack
laser
white paper
masking tape
lamp
Procedure
This experiment must be performed in the dark. The wavelength of the laser is 630-680 nm.
Measure L to the nearest mm. Measure the distances between minima to the nearest mm.
1.
Use the narrower single and double slit on the slit slide. Mount the slide in the holder
parallel to the wall. Measure L, the distance from the slit to the wall.
2.
Turn out the lights. Use the rubber band to keep the laser pointer on and mount it in the
holder. Shine the laser through the single slit and adjust it until a clear pattern appears on
the wall. Tape a piece of white paper on the wall where the pattern appears.
3.
Mark the center of the diffraction pattern and mark the center of each minimum.
4.
Repeat the procedure using the double slit. Note the single slit pattern superimposed on the
double slit pattern; the center of the pattern is not hard to find.
5.
When everyone has done this part you can turn on the lights. Take down the paper.
Measure the width of groups of three or four minima for the data from each slit or set of
slits. Record the distances and how many minima were in the group. This technique,
called the method of differences, will give better results than either measuring the distances
between individual minima or simple measuring from one end of the pattern to the other.
6.
Have your instructor check your data.
7.
Put your equipment away carefully
Data
Data will consist of the distance from the slit to the wall (L), the wavelength of the laser, the
widths of the groups of minima and the number of minima for each measurement.
Analysis
Use the average of the range of wavelengths for the laser.
1.
2.
Find the average distance between minima for the single and double slit.
y
to find a and d for m = 1 .
L
Compare these to the accepted value of a= 0.1 mm and d = 0.2 mm .
Call this value y. Use the approximation sinθ = tanθ =
Questions
1.
Write at least one paragraph in which you define diffraction and interference, discuss
Huygens' Principle and explain why light passing through a narrow slit or set of fine slits
will produce a pattern on a wall.
2.
Diode lasers produce a range of wavelengths. Do you think using the average made much
difference in your calculations? Explain in detail.
3.
How would the pattern on the wall have been different if you had used a helium-neon laser
which only produces light of one wavelength?
4.
What would the diffraction pattern look like if the light you used was composed of several
specific wavelengths?
5.
In order to have a clear diffraction pattern the slit must be around the same order of
magnitude as, but not smaller than the wavelength of the light. What is the ratio of single
slit width to wavelength for your experiment? How would the pattern on the wall change if
you could gradually widen the slit?
If it applies to you, write "I have not cheated on this lab report" and sign your name.
Grading
4 pts
Data and Analysis.
4 pts
Each for question 1.
3 pts
Each for questions 2, 3, 4, and 5.