Optics and Wave Phenomena
Optics and Wave Phenomena is about 9% of the GRE Physics Subject Test. It mixes geometric optics (mirrors, lenses, refraction, total internal reflection) with physical optics (interference, diffraction, polarization) and general wave behavior such as superposition, standing waves, beats, and the Doppler effect.
Core rules
- Reflection: angle of incidence equals angle of reflection. Refraction: n₁ sinθ₁ = n₂ sinθ₂, with v = c/n and λ_medium = λ_vacuum/n.
- Total internal reflection occurs only from higher to lower index, at sinθ_c = n₂/n₁.
- Thin lens and spherical mirror: 1/f = 1/d_o + 1/d_i, magnification m = −d_i/d_o. Sign conventions must be applied consistently; a virtual image has negative d_i for a lens.
- Two-source interference: constructive when the path difference is mλ, destructive when it is (m + ½)λ. For a double slit, bright fringes at d sinθ = mλ and spacing Δy = λL/d on a distant screen.
- Thin films: a phase flip occurs on reflection only when going from lower to higher n, so the condition becomes 2nt = mλ or 2nt = (m + ½)λ depending on the number of flips.
- Single-slit diffraction minima satisfy a sinθ = mλ (m ≠ 0); a grating has maxima at d sinθ = mλ. Rayleigh resolution: θ_min = 1.22λ/D.
- Polarization: Malus's law I = I₀cos²θ after a polarizer; Brewster angle tanθ_B = n₂/n₁.
Worked example
Light of λ = 500 nm passes through a double slit with d = 0.20 mm and falls on a screen 2.0 m away. The fringe spacing is Δy = λL/d = (500×10⁻⁹ × 2.0)/(2.0×10⁻⁴) = 5.0×10⁻³ m, so bright fringes are 5.0 mm apart. The third-order maximum sits at sinθ = 3λ/d = 7.5×10⁻³, or θ ≈ 0.43°.
Traps
Mixing up the single-slit minimum condition with the double-slit maximum condition; forgetting the reflection phase flip in thin-film problems; using the vacuum wavelength inside a medium; inserting the wrong sign for a virtual image; confusing angular fringe width with linear fringe spacing; applying small-angle approximations where sinθ is not small.