# Single-Slit Laser Diffraction

```Single-Slit Laser Diffraction
Introduction
When monochromatic light is incident on a single aperture, the light waves interfere with one another
(diffract) and cause alternating light and dark bands on a distant screen. The angles where dark bands
(destructive interference) occur can be predicted as follows:
a*sin(θ) = pλ
a = aperture size
θ =angular location of dark spot as measured
from a straight line
p = 1, 2, 3 …
λ = wavelength of light
If the angles are small, then the following approximation can be used:
sin(θ) ≈ θ ≈ y/L
y = location of dark band on screen as
measured from the center
L = distance from aperture
Combining the small angle approximation with the condition for destructive interference yields the
following locations for dark bands:
ay/L = pλ
y = pλL/a
The size of the central bright band will be double the distance from the center to the first dark band:
w = 2λL/a
The purpose of this lab is to use this equation to calculate the wavelength of a laser.
Experimental Procedures
1) If you use metal calipers, then place masking tape on the broad side of them. This will make
reflections diffuse and help protect your eyes. Don’t wrap the tape around the inside of the
calipers.
2) Clamp the calipers to an aluminum post and open them to at most 0.50 mm. This is the aperture
size, a. There should be a large distance between the calipers and a wall.
3) Measure the distance between the calipers and the wall, L.
4) Aim a laser near the tips of the calipers and observe the single-slit diffraction pattern on the wall.
Be very careful to avoid hitting anyone in the eyes with the laser.
5) Carefully measure the width of the central bright spot, w. This is the distance between the centers
of the dark spots on either side of the central bright spot (see the figure above). It is NOT simply
the perceived width of the dot.
6) Turn off the laser.
7) Calculate the wavelength of the laser light and compare it to the accepted value. Helium-neon
lasers generate light with a wavelength of 632.8 nm. Other lasers will be labeled.
8) Repeat steps 2 through 7 using different lasers (green or blue), aperture sizes, or distances to the
wall. Perform a total of 4 experiments.
```