Law

Snell's law

n_{1} sin θ_{1} = n_{2} sin θ_{2}

Statement

Relates the angles of incidence and refraction at a boundary between two media of refractive index n₁ and n₂.

Symbols and units

$n_{1}, n_{2}$	refractive indices of the two media	—
$θ_{1}, θ_{2}$	angle of incidence, refraction	degrees

When it applies

A smooth boundary between two transparent, homogeneous media.

Don't use when

Requires a smooth boundary between two transparent, homogeneous media — a rough or gradient-index boundary needs a different treatment.

Derivation

Derivable from Fermat's principle of least time, or from the wave picture of light slowing in a denser medium; empirically confirmed directly as well.

n_{1} sin θ_{1} = n_{2} sin θ_{2}, n = \frac{c}{v}

Worked examples

The limit of a very dense medium

As n₂ → ∞, for any angle of incidence:

sin θ_{2} = \frac{n _{1}}{n _{2}} sin θ_{1} \to 0

The refracted ray bends almost exactly onto the normal, regardless of how the light entered — an extremely dense medium funnels light straight through.

Watch out for

Light bends TOWARD the normal entering a denser medium (higher n), and AWAY from the normal entering a less dense one — easy to reverse.