Oscillations, Waves, and Optics
Core concepts
Simple harmonic motion (SHM) occurs when restoring force is proportional to displacement: F = −kx. Then a = −ω²x, with ω = 2π/T. For a mass–spring system, T = 2π√(m/k); for a simple pendulum, T = 2π√(ℓ/g). Energy oscillates between kinetic and potential, with total energy constant (for an ideal oscillator).
Waves transfer energy without transferring matter. Key parameters: wavelength λ, frequency f, speed v = λf. Sound is longitudinal; light is transverse. Interference depends on path difference; constructive when Δ = nλ, destructive when Δ = (n + ½)λ. Standing waves on strings and in pipes have quantized frequencies.
Optics: reflection obeys equal angles; refraction obeys Snell's law, n₁sinθ₁ = n₂sinθ₂. The refractive index n = c/v. Total internal reflection occurs beyond the critical angle. Lenses and mirrors follow 1/f = 1/dₒ + 1/dᵢ, with sign conventions. Young's double slit gives fringe spacing Δy = λL/d.
Traps
- Using degrees instead of radians in SHM equations.
- Confusing period and frequency.
- Forgetting to use consistent units in v = λf.
- Sign errors in lens/mirror formulas.
- Applying the critical-angle formula only when light goes from denser to rarer medium.
Worked rule of thumb
For a pendulum, quadrupling the length doubles the period - a quick sanity check for √ proportionality.