Waves and Optics
Waves and Optics covers wave properties, sound, geometric optics, and interference. Questions often combine a conceptual check with a short calculation, so units and the small-angle approximation matter.
Core rules
- Wave basics. v = fλ. When a wave enters a new medium, frequency is unchanged while speed and wavelength change.
- Sound. v ≈ 343 m/s in air at 20 °C. Doppler shift: f′ = f(v ± v_o)/(v ∓ v_s).
- Standing waves. String fixed at both ends: fₙ = nv/(2L). Open pipe: fₙ = nv/(2L). Pipe closed at one end: fₙ = nv/(4L) for odd n only.
- Refraction. n₁ sin θ₁ = n₂ sin θ₂ with n = c/v. Total internal reflection occurs when θ₁ exceeds θ_c = sin⁻¹(n₂/n₁).
- Double slit. Bright fringes at d sin θ = mλ, or y ≈ mλL/d for small angles.
Worked example
A 600 nm laser illuminates a double slit with d = 0.20 mm; the screen is 2.0 m away. The first bright fringe sits at y = λL/d = (600 × 10⁻⁹)(2.0)/(2.0 × 10⁻⁴) = 6.0 × 10⁻³ m = 6.0 mm from the central maximum, and every subsequent fringe is spaced 6.0 mm farther out.
Traps
- Feeding degrees into y = mλL/d, which is derived for small angles.
- Claiming the frequency of light changes when it enters glass.
- Swapping the 2L and 4L formulas between open and stopped pipes.
- Mixing image types: a real image from a converging lens is inverted and on the far side; a virtual image is upright and on the object side.