Waves, Oscillations and Optics
Waves, Oscillations and Optics links simple harmonic motion to wave behaviour and then to light. Questions typically ask you to calculate a period, wavelength or fringe spacing, and to explain refraction, total internal reflection, interference and diffraction.
Oscillations
For SHM, acceleration is proportional to displacement and opposite in direction: a = −ω²x, with ω = 2πf = 2π/T. A simple pendulum has T = 2π√(l/g); a mass on a spring has T = 2π√(m/k). Period is independent of amplitude for small oscillations.
Waves
v = fλ. Frequency is fixed by the source; speed depends on the medium. On refraction into a denser medium, frequency stays the same while speed and wavelength decrease. In a stationary wave the node-to-node distance is λ/2; for a string fixed at both ends the fundamental has λ = 2L.
Optics
Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Critical angle: sin c = 1/n for glass to air. For a thin lens, 1/f = 1/u + 1/v using the real-is-positive convention, and magnification m = v/u. Young's double slit gives fringe spacing w = λD/d, where d is the slit separation, not the slit width. A diffraction grating obeys d sin θ = nλ.
Worked example
Light of wavelength 589 nm falls on two slits 0.50 mm apart; the screen is 1.20 m away. w = λD/d = (589 × 10⁻⁹ × 1.20)/(0.50 × 10⁻³) = 1.41 × 10⁻³ m = 1.41 mm.
Traps
Entering nm or mm without converting; using slit width for d; mixing degrees and radians; claiming frequency changes on refraction; dropping the minus sign in a = −ω²x, which signals the restoring direction.