Electromagnetic Waves and Optics
This domain covers Maxwell's displacement current, the electromagnetic spectrum, and ray and wave optics through interference, diffraction and polarisation.
Core rules
- Displacement current I(d) = ε₀ dΦ(E)/dt restores continuity of current while a capacitor charges.
- EM waves are transverse with E ⊥ B ⊥ direction of propagation; E₀/B₀ = c and c = 1/√(μ₀ε₀) ≈ 3×10⁸ m s⁻¹.
- Spectrum in order of increasing wavelength: gamma, X-ray, ultraviolet, visible, infrared, microwave, radio.
- Refraction: n₁ sin i = n₂ sin r; critical angle sin C = 1/n for denser-to-rarer travel.
- Huygens' principle yields reflection and Snell's law; interference is bright when the path difference is nλ.
- Young's double slit: fringe width β = λD/d.
- Single-slit diffraction minima: a sinθ = mλ. Polarisation by reflection follows Brewster's law, tan i(p) = n.
Worked example
In a Young's double-slit set-up λ = 600 nm, d = 1.0 mm and D = 1.0 m. Then β = λD/d = (600×10⁻⁹ × 1.0)/(1.0×10⁻³) = 6.0×10⁻⁴ m = 0.60 mm. Immersing the apparatus in water (n = 4/3) shortens the wavelength to λ/n, so the fringe width falls to 0.45 mm.
Traps
Ignoring sign conventions in the lens formula; confusing two-source interference with single-aperture diffraction; forgetting that fringe width depends on the wavelength in the medium, not in vacuum; using degrees where the small-angle approximation needs radians.