Waves and Optics
What this domain tests
This domain covers wave properties, superposition, stationary waves, interference, diffraction, refraction, lenses and optical instruments. GCE questions typically ask you to relate path difference to phase, use the grating and lens equations correctly, and explain fringe patterns in terms of superposition.
Core wave relations
- v = fλ; intensity is proportional to amplitude²; polarisation is possible only for transverse waves.
- Phase difference = 2π × (path difference)/λ.
- Superposition: displacements add vectorially. Two identical waves travelling in opposite directions give a stationary wave with nodes every λ/2 and adjacent node–antinode spacing λ/4. No net energy is transported.
- Young's double slit: fringe spacing x = λD/a, where a is the slit separation and D the slit-to-screen distance.
- Diffraction grating: d sinθ = nλ, with d = 1/N and N the number of lines per metre.
Refraction and lenses
Snell's law n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v; critical angle sinθc = 1/n (only when moving to a less dense medium). For lenses use 1/f = 1/u + 1/v with a consistent real-is-positive convention, and m = v/u = image height/object height. A convex lens converges; a concave lens diverges and gives a virtual, diminished image.
Worked example
A grating has 500 lines per mm. Find the angle of the second-order maximum for light of wavelength 589 nm.
d = 1/(500 × 1000) = 2.0 × 10⁻⁶ m. sinθ = nλ/d = (2 × 589 × 10⁻⁹)/(2.0 × 10⁻⁶) = 0.589. θ = 36.1°.
Traps that cost marks
- Using degrees inside small-angle formulae that require radians.
- Confusing the order n in d sinθ = nλ with a refractive index.
- Mixing sign conventions in 1/f = 1/u + 1/v, then reporting a virtual image as real.
- Claiming a stationary wave transfers energy along the string.
- Confusing path difference with phase difference (a factor of 2π/λ).
- Forgetting that sinθ ≤ 1 sets a maximum observable order.