Waves, Optics, and Thermodynamics
Waves, Optics, and Thermodynamics
This domain tests wave properties and superposition, sound and light behavior, geometric and physical optics, and the laws of heat, temperature, and ideal gases.
Core rules
- Wave relation: v = fλ. Frequency is set by the source; speed depends on the medium. In a standing wave on a string fixed at both ends, λₙ = 2L/n.
- Sound: intensity level β = 10 log(I/I₀), with I₀ = 10⁻¹² W/m². The Doppler shift raises observed frequency when source and observer approach.
- Refraction: n₁ sinθ₁ = n₂ sinθ₂, with angles measured from the normal. Light bends toward the normal entering a denser medium. Total internal reflection occurs above the critical angle, sinθc = n₂/n₁.
- Thin lenses and mirrors: 1/f = 1/d₀ + 1/dᵢ; magnification m = −dᵢ/d₀. Real images form on the outgoing-light side of a lens; virtual images have negative dᵢ.
- Thermodynamics: ΔU = Q − W for work done by the gas. For an ideal gas, PV = nRT. Specific heat Q = mcΔT; latent heat Q = mL. Entropy increases in irreversible processes.
Worked example
Light in air (n = 1.00) strikes glass (n = 1.50) at 30.0° from the normal. Find the refracted angle. Snell's law gives sinθ₂ = (1.00/1.50) sin30.0° = 0.333, so θ₂ ≈ 19.5°. The ray bends toward the normal because the glass is optically denser. The frequency is unchanged; the wavelength shortens by a factor of 1.50.
Traps
- Measuring refraction angles from the surface instead of the normal.
- Reversing the Doppler shift for an approaching source.
- Using the lens equation with dᵢ negative for a real image.
- Confusing heat with temperature; a large sample can contain more thermal energy at the same temperature.
- Forgetting that work in ΔU = Q − W is work done by the system.