Optics and Thermal Physics
This domain combines ray optics with thermal physics. For optics, expect Snell’s law, total internal reflection, thin lenses and magnification. For thermal physics, expect specific heat capacity, latent heat, the ideal gas equation, kinetic theory and the first law of thermodynamics.
Core rules
- Snell’s law: n1 sin θ1 = n2 sin θ2. Critical angle: sin c = n2/n1 when n1 > n2.
- Thin lens equation: 1/f = 1/u + 1/v, with a consistent sign convention; magnification m = v/u or −v/u in the Cartesian convention.
- Q = mcΔT for temperature change; Q = mL for a phase change at constant temperature.
- Ideal gas: pV = nRT; average kinetic energy of a molecule is 3/2 kT for a monatomic gas.
- First law: ΔU = Q − W if W is work done by the gas. Adiabatic means Q = 0; isothermal means ΔU = 0 for an ideal gas.
Worked example
An object is 30 cm from a converging lens of focal length 10 cm. Using 1/v = 1/f − 1/u = 1/10 − 1/30 = 1/15, so v = 15 cm. The image is real, inverted and diminished; magnification m = 15/30 = 0.50. Check the sign convention: with the real-is-positive convention, a positive v confirms a real image on the opposite side.
Traps
- Mixing real-is-positive and Cartesian sign conventions mid-calculation.
- Using degrees in a calculator set to radians, or vice versa.
- Applying Q = mcΔT during melting or boiling.
- Using Celsius temperatures in pV = nRT; use kelvin.
- Confusing work done by the gas with work done on the gas in the first law.