Example from Physics, 17.1 Understanding Diffraction and Interference

Single-Slit Diffraction

Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0° relative to the incident direction of the light. What is the width of the slit?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
From the given information, and assuming the screen is far away from the slit, you can use the equation $D \sin θ = m λ$ to find D.
Solution
Quantities given are $λ$ = 550 nm, m = 2, and $θ_{2}$ = 45.0°. Solving the equation $D \sin θ = m λ$ for D and substituting known values gives
$D = \frac{m λ}{sin θ} = \frac{2 (550 nm)}{sin 45.0°} = 1.56 \times 10^{−6} m.$
17.4

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Strategy

Solution