Superposition and diffraction

When waves meet they add together: superposition. In step they reinforce (constructive), out of step they cancel (destructive). Waves also spread out through gaps: diffraction.

Key facts

  • Path difference of nλ: constructive; (n + ½)λ: destructive.
  • Diffraction is greatest when the gap is about the same size as the wavelength.
  • Diffraction grating: d sin θ = nλ.
  • Standing waves form when two identical waves travel opposite ways.

Worked examples

Example 1

Light of wavelength 600 nm passes through a grating with 500 lines per mm. Find the angle of the first-order maximum.

  1. d = 1/500 mm = 2 × 10⁻⁶ m
  2. sin θ = 600 × 10⁻⁹ ÷ 2 × 10⁻⁶ = 0.3 θ ≈ 17.5°

Answer: 17.5°