Electromagnetic Waves and Optics (Ray Optics and Wave Optics)
A large unit combining the nature and spectrum of EM waves with ray optics (mirrors, lenses, refraction, total internal reflection, prisms, optical instruments) and wave optics (Huygens' principle, Young's double slit, single-slit diffraction, polarisation). Expect at least one long answer here - lens formula mapping, prism formula, or interference fringe derivation - plus short numericals on fringe width, critical angle, power of a lens or resolving ability.
Core rules
- EM waves are transverse, with E ⊥ B ⊥ direction of propagation; c = 1/√(μ₀ε₀) and E₀/B₀ = c. They carry momentum and need no medium.
- Spectrum order by decreasing wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
- Mirror: 1/v + 1/u = 1/f, f = R/2. Lens: 1/v − 1/u = 1/f; power P = 1/f (dioptre, f in metres).
- Refraction: n₁sin i = n₂sin r; critical angle sin C = 1/n; TIR requires light going from denser to rarer at i > C.
- Prism: n = sin[(A + δm)/2] / sin(A/2).
- Young's double slit: fringe width β = λD/d, and path difference nλ for bright, (2n−1)λ/2 for dark fringes.
- Polarisation by reflection (Brewster): tan i(p) = n.
Worked example
In a Young's double-slit experiment λ = 600 nm, slab-to-screen distance D = 1 m and slit separation d = 0.5 mm. Find the fringe width. β = λD/d = (600×10⁻⁹ × 1)/(0.5×10⁻³) = 1.2×10⁻³ m = 1.2 mm. Reasoning check: since β ∝ λ, immersing the whole apparatus in water (n ≈ 1.33) reduces λ inside the medium and shrinks β to about 0.9 mm; increasing d would likewise reduce β.
Traps that cost marks
- Sign-convention errors in the lens and mirror formulas; keep one convention (Cartesian, distances measured from the pole/optical centre) throughout.
- Forgetting that fringe width increases with D and with λ, but decreases with d.
- Confusing interference (two coherent sources, equal-width fringes) with diffraction (single slit, central maximum twice as wide).
- Stating that TIR occurs when light goes from rarer to denser medium.