Waves and Optics
Waves and Optics: what is tested
This domain covers wave properties, sound, geometric optics, and interference and diffraction. The exam tests the wave equation, refraction and lenses, and path-difference reasoning, often with a calculation followed by a direction or condition question.
Core rules
- Wave speed v = fλ. Frequency is set by the source and stays constant when a wave enters a new medium; speed and wavelength change.
- Sound is longitudinal; in air its speed depends mainly on temperature. Intensity from a point source falls as 1/r². The Doppler shift depends on relative motion between source and observer.
- Refraction follows Snell's law: n₁ sinθ₁ = n₂ sinθ₂. The critical angle satisfies sinθ_c = n₂/n₁ when n₁ > n₂.
- For thin lenses and spherical mirrors, 1/f = 1/d_o + 1/d_i, with magnification m = −d_i/d_o. Use one sign convention consistently.
- Two-source interference depends on path difference: constructive when Δ = mλ, destructive when Δ = (m + ½)λ.
- Young's double slit gives fringe spacing Δy = λD/d. A diffraction grating has maxima at d sinθ = mλ.
Worked example
In a double-slit experiment, λ = 600 nm, slit separation d = 0.20 mm, and screen distance D = 2.0 m. The fringe spacing is Δy = λD/d = (600 × 10⁻⁹ × 2.0)/(0.20 × 10⁻³) = 6.0 × 10⁻³ m, or 6.0 mm. The third bright fringe is therefore about 18 mm from the central maximum. The small-angle approximation is reasonable because 6 mm is much less than 2.0 m.
Traps that cost marks
Keep degrees and radians consistent. Do not assume frequency changes on refraction. In ray diagrams, a virtual image has a negative image distance under the common Cartesian convention. For interference, compare path differences in the same medium and remember that a phase reversal on reflection can add a half-wavelength shift. Diffraction is significant only when the aperture is comparable to the wavelength. Do not use the double-slit spacing formula for a diffraction grating without accounting for d sinθ = mλ.