Ray Optics & Lenses

Reflection: angle of incidence = angle of reflection. Both measured from the normal.

Refraction: Snell's law — n₁ sin θ₁ = n₂ sin θ₂. Light bends toward normal when entering a denser medium.

Total internal reflection occurs when light goes from denser to rarer medium at angle > critical angle (sin θc = n₂/n₁).

Mirror equation: 1/f = 1/v + 1/u. Sign convention: distances are measured from the pole.

Lens equation: 1/f = 1/v − 1/u (thin lens formula).

Magnification: m = v/u (mirrors) or m = v/u (lenses). Negative m means inverted image.

Lensmaker's equation: 1/f = (n−1)(1/R₁ − 1/R₂) for a thin lens in air.

Power of a lens: P = 1/f (in diopters when f is in meters). Converging lens: +P, diverging: −P.