Waves, Optics, and Acoustics
Core concepts
Wave fundamentals: v = fλ, superposition, and the distinction between transverse and longitudinal waves. Sound intensity follows the inverse-square law and decibels use 10 log₁₀(I/I₀), with I₀ = 10⁻¹² W/m². For standing waves, nodes and antinodes, harmonics on strings and in pipes (open–open versus closed–open differ in allowed frequencies). Optics: reflection, refraction with Snell's law n₁sinθ₁ = n₂sinθ₂, total internal reflection beyond the critical angle sinθ_c = n₂/n₁, thin lenses and mirrors via 1/f = 1/d_o + 1/d_i with magnification m = −d_i/d_o. Interference and diffraction: double-slit maxima at d sinθ = mλ, single-slit minima at a sinθ = mλ, and thin-film phase shifts of half a wavelength on reflection from a higher-index medium.
Traps
Sign conventions for lenses are the most common error-real images have positive d_i in the standard convention. Do not confuse single-slit minima with double-slit maxima. Doppler formulas differ for moving source versus moving observer. In pipes, a closed end is a displacement node but a pressure antinode. Remember the half-wavelength phase flip on reflection matters for thin films.
Worked example
Light of 600 nm passes a double slit with d = 0.30 mm. The first-order maximum is at sinθ = λ/d = 2×10⁻³, so θ ≈ 0.11°. Rule of thumb: small-angle approximations sinθ ≈ tanθ ≈ θ (radians) simplify fringe spacing to Δy = λL/d.