Mastering Physics Solutions: ± Single-Slit Diffraction

Single-Slit Diffraction

Part A = 170 μm
Part B = The width would decrease.

Solution Below:

You have been asked to measure the width of a slit in a piece of paper. You mount the paper 80.0 centimeters from a screen and illuminate it from behind with laser light of wavelength 633 nanometers (in air). You mark two of the intensity minima as shown in the figure, and measure the distance between them to be 17.9 millimeters.

Part A

What is the width α of the slit?

Since we’re measuring the distance between minima for a single slit diffraction, the formula to use is a*sin(θ) = m * λ. In this problem, the distance between minima was measured between the 3rd order minima, so n = 3. Now figure out what θ is. Since the distance between the minima is 17.9mm, divide that in half and use it as the base of your triangle (8.95mm). The distance from the screen (80.0 cm) forms the side. We can say that the sin = tan for this angle, or use small angle approximation, which gives us a sin of 8.95mm / 80.0cm, or 0.00895 / 0.800 = 0.0111875

a*sin(θ) = m * λ
a * 0.0111875 = 3 * 633 * 10^-9
a = 1.6974 * 10^-4 m
a = 170μm

170 μm

Part B

If the entire apparatus were submerged in water, would the width of the central peak change?

• The width would increase.
• The width would decrease.
• The width would not change.

Since water has a higher index of refraction than air, the wavelength of light decreases in water, relative to air, and the width of the central peak will decrease, too.

The width would decrease.

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