← Wave Systems

7 Diffraction & refraction

Diffraction grating

Grating equation d sin θ = n λ d = 1/(lines per metre). Sharper, brighter maxima than double slit.

⭐ Counting maxima, and which colour sits closest to the centre

  • The central maximum is n = 0, straight through. Orders then appear symmetrically on both sides.
  • So a total of 7 maxima means the central one plus 3 either side (2025). Always say “either side of the central maximum” — the schedules require it.
  • For the highest order visible, set sin θ = 1 in d sin θ = nλ, so nmax = d/λ, then round down to a whole number.
  • Which colour is closest to the centre? Smaller λ → smaller θ for the same order. Violet/blue diffracts least and sits nearest the central maximum; red sits furthest out.
✕

Sound entering a new medium: the speed is what changes, not the frequency

When a wave crosses into a different medium its frequency is fixed by the source and does not change — the speed changes, and λ changes with it (v = fλ).

But watch the direction of the question: in Doppler problems the source and observer move through one medium, so the speed of sound stays constant (343 m s⁻¹) and it is the observed frequency that changes. The 2023, 2024 and 2025 schedules all award a mark for stating that the speed of sound is unchanged. Do not mix the two situations up.

Refraction: Snell’s law

Snell’s law n₁ sin θ₁ = n₂ sin θ₂ n = refractive index. Light bends toward the normal entering a denser medium. Refractive index n=\frac{c}{v} c = speed of light in vacuum; v = speed in the medium. Critical angle \sin\theta_c=\frac{n_2}{n_1} Beyond θ_c: total internal reflection (n₁ > n₂).

Practise just this