• Tags: refraction, curved-surface, snell
• Difficulty: Moderate

When light refracts at a single curved surface separating media of refractive indices $n_{1}$ and $n_{2}$:

$n_{2}$/v - $n_{1}$/u = $\frac{n_{2} - n_{1}}{R}$

This is derived by applying Snell's law at a single refracting surface using the paraxial ray approximation (sin θ ≈ θ for small angles).

Key points: R is positive if the centre of curvature is on the transmission side, negative otherwise. This formula is the foundation for deriving the lens maker's equation.