Sound and Optics
Core concepts
Sound: speed in gases (v = √(γRT/M)), intensity and decibels, resonance, and the Doppler effect. Optics: reflection, refraction, Snell's law, total internal reflection, lenses and mirrors (1/f = 1/v + 1/u), magnification, interference (Young's double slit), diffraction gratings, and polarisation.
Traps
- Applying the mirror/lens formula with inconsistent sign conventions; pick one convention and stick to it.
- Forgetting that the critical angle exists only when light travels from denser to rarer medium.
- Mixing up constructive and destructive path differences: mλ vs (m + ½)λ.
- Treating sound intensity as amplitude rather than amplitude squared.
- Forgetting that a diffraction grating produces sharp maxima at d sinθ = mλ.
Rule of thumb
Critical angle: sin C = n₂/n₁ (n₁ > n₂). For a thin lens, magnification m = v/u with the sign convention you adopt.
Worked example
Light of wavelength 600 nm falls on a grating with 500 lines per mm. Slit spacing d = 1/(500 × 10³) = 2×10⁻⁶ m. First-order maximum: sinθ = λ/d = 600×10⁻⁹/2×10⁻⁶ = 0.30, so θ ≈ 17.5°. Second-order: sinθ = 0.60, θ ≈ 36.9°.