Electromagnetic Waves and Optics
Electromagnetic Waves and Optics covers displacement current, the EM spectrum, reflection, refraction, lenses and mirrors, interference, diffraction and polarisation. Ray optics numericals and wave-optics reasoning both appear.
Core rules
- Maxwell's displacement current I_d = ε₀ dΦ_E/dt makes the circuit continuity law complete and predicts EM waves. In vacuum c = 1/√(μ₀ε₀); E/B = c.
- EM waves are transverse; E, B and propagation direction are mutually perpendicular. The spectrum runs radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
- Snell's law n₁ sin i = n₂ sin r. Total internal reflection needs light going from denser to rarer medium and i > i_c, with sin i_c = n₂/n₁.
- Lens/mirror formula: 1/v - 1/u = 1/f (Cartesian sign convention for lenses); magnification m = v/u. Power P = 1/f in dioptres with f in metres.
- Young's double slit: fringe width β = λD/d. Polarisation proves transverse nature; diffraction limits resolution.
Worked example
An object is 30 cm from a convex lens of focal length 20 cm. Using 1/v - 1/u = 1/f with u = -30 cm, 1/v = 1/20 + 1/(-30) = 1/60, so v = +60 cm. The image is real, on the other side, and magnification m = v/u = 60/(-30) = -2: inverted and twice the size.
Traps
Ignoring sign conventions; using n = sin i/sin r with angles measured from the surface rather than the normal; and confusing fringe width with slit separation.