Real-is-positive convention: f > 0 for converging lenses, f < 0 for diverging lenses. A real object has u > 0. A real image has v > 0; a virtual image has v < 0.
Thin-lens equation: 1/f = 1/u + 1/v, with all distances in the same units (cm).
Magnification: m = −v/u. Negative m means inverted; positive m means upright. Image height divided by object height gives m.
Power: P = 1/f in metres, measured in dioptres (D). A positive power converges light.
Snell's law: n₁ sin θ₁ = n₂ sin θ₂. At parallel interfaces, n sin θ is conserved until total internal reflection occurs.
Critical angle: sin C = n₂/n₁ for n₁ > n₂. At C the transmitted angle is 90°. Beyond C there is no propagating transmitted ray.
Assumptions: Thin lenses, paraxial rays, homogeneous transparent media, parallel plane interfaces and monochromatic light. Angles are measured from the normal.