Waves and Optics
Domain 4: Waves and Optics
Waves and Optics covers wave properties, superposition, standing waves, sound, the Doppler effect, reflection and refraction, lenses and mirrors, and interference and diffraction. Ray diagrams and sign conventions matter as much as formulas.
Core rules
- v = fλ; frequency is set by the source and does not change on refraction; speed and wavelength do.
- Standing waves: nodes are separated by λ/2; strings fixed at both ends have λn = 2L/n; open pipes use the same set, while closed pipes use odd harmonics.
- Snell's law: n1 sinθ1 = n2 sinθ2; n = c/v. Total internal reflection occurs only going from higher to lower n, beyond θc = sin⁻¹(n2/n1).
- Thin lens or mirror: 1/f = 1/do + 1/di; magnification m = −di/do. Real images form where rays converge.
- Double slit: bright fringes at d sinθ = mλ; single-slit minima at a sinθ = mλ (m ≠ 0). Thin-film interference depends on phase reversal at boundaries.
Worked example
Light of 633 nm passes through two slits 0.050 mm apart onto a screen 2.0 m away. Fringe spacing Δy = λL/d = (633×10⁻⁹)(2.0)/(5.0×10⁻⁵) = 2.5×10⁻² m = 2.5 cm. The second bright fringe is 2Δy = 5.1 cm from the center. The small-angle approximation sinθ ≈ tanθ ≈ y/L is justified here.
Traps
- Reversing the bright and dark conditions for double versus single slits.
- Expecting total internal reflection at any angle or from low to high index.
- Forgetting that a converging lens forms a virtual image when the object is inside f.
- Mixing degrees and radians in d sinθ = mλ.
- Claiming the Doppler shift changes source frequency rather than observed frequency.