Diffraction Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Light of wavelength 600 nm600 \text{ nm} passes through a single slit of width 0.1 mm0.1 \text{ mm}. At what angle does the first minimum of the diffraction pattern occur?

Solution

  1. 1
    For single-slit diffraction, minima occur at: asin⁡θ=mλa\sin\theta = m\lambda, where m=1,2,3,...m = 1, 2, 3, ...
  2. 2
    For the first minimum (m=1m = 1): sin⁡θ=λa=600×10−90.1×10−3=6×10−710−4=6×10−3\sin\theta = \frac{\lambda}{a} = \frac{600 \times 10^{-9}}{0.1 \times 10^{-3}} = \frac{6 \times 10^{-7}}{10^{-4}} = 6 \times 10^{-3}.
  3. 3
    θ=sin⁡−1(0.006)≈0.34°\theta = \sin^{-1}(0.006) \approx 0.34°

Answer

θ≈0.34°\theta \approx 0.34°
When light passes through a narrow slit, it diffracts and creates a pattern of bright and dark fringes. The first dark fringe occurs at an angle that depends on the ratio of wavelength to slit width.

About Diffraction

The spreading of a wave as it passes through a gap or around the edge of an obstacle.

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