Waves and Optics
What Waves and Optics tests
This domain tests wave speed, frequency, and wavelength; superposition and standing waves; sound; reflection and refraction; lenses and mirrors; and interference and diffraction. The exam favors proportionality reasoning and ray or path-difference analysis described in words.
Core rules
- v = fλ. For a stretched string v = √(T/μ); for sound in air, speed depends mainly on temperature.
- Refraction obeys Snell’s law, n1 sinθ1 = n2 sinθ2, with n = c/v. Frequency stays constant across an interface; wavelength and speed change.
- Thin-lens/mirror equation: 1/f = 1/do + 1/di, with magnification m = −di/do. Use a consistent sign convention.
- Constructive interference for two coherent sources occurs when path difference is mλ; destructive when it is (m + 1/2)λ.
- In a double slit, fringe spacing is Δy = λL/d for small angles.
Worked example
Light of wavelength 600 nm passes through two slits 0.20 mm apart and strikes a screen 2.0 m away. Find the spacing between adjacent bright fringes.
Convert: λ = 600 × 10^−9 m = 6.0 × 10^−7 m, d = 2.0 × 10^−4 m, L = 2.0 m. Δy = λL/d = (6.0 × 10^−7)(2.0)/(2.0 × 10^−4) = 6.0 × 10^−3 m. The fringes are 6.0 mm apart. The small-angle approximation is reasonable because λ/d = 0.003.
Traps
Using degrees in a formula requiring radians; changing frequency at a boundary; mixing sign conventions for real and virtual images; calling intensity proportional to amplitude rather than amplitude squared; using the slit separation as the distance to the screen.