Optics: Geometric, Interference, Diffraction, Polarization
Core concepts
Geometric optics: reflection, Snell's law (n₁ sinθ₁ = n₂ sinθ₂), total internal reflection (sinθ_c = n₂/n₁), thin-lens and mirror equations (1/f = 1/u + 1/v with a stated sign convention), magnification. Interference: Young's double slit, path difference, constructive (mλ) and destructive ((m+½)λ) conditions, thin-film interference including phase shift on reflection. Diffraction: single-slit minima at a sinθ = mλ, diffraction grating maxima at d sinθ = mλ. Polarization: Malus's law (I = I₀ cos²θ), Brewster's angle (tanθ_B = n₂/n₁).
Traps
- Sign conventions in the lens equation - fix one before starting.
- Forgetting the π phase shift on reflection from a denser medium.
- Confusing single-slit minima with double-slit maxima.
- Using the small-angle approximation outside its range.
- Mixing up Brewster's angle with critical angle.
Worked example
A grating has 500 lines/mm, so d = 2 × 10⁻⁶ m. For λ = 500 nm, first-order maximum: sinθ = λ/d = 0.25, so θ ≈ 14.5°. Rule of thumb: if sinθ > 1, that order does not exist - a common sanity check.