Snell's Law

Snell’s Law, or law of refraction, describes the relationship between the angles of incidence and refraction index in refraction.

The law states that for a given pair of media with refractive indices and , the relationship of the sines of incidence angle and the refraction angle is

From the equation, we can see that a larger refractive index corresponds to a smaller value of (and thus a smaller angle ), meaning the light is bent more toward the normal.

Snell’s Law can be derived by Fermat’s principle. ¹

An observation with Snell’s Law is that it doesn’t depend on specific values of the refractive indices, but rather on their ratio. In other words, we can simplify the Snell’s Law into

where ¹

Note that Snell’s Law doesn’t always have a solution. When it does not have a solution, total internal reflection happens.

Footnotes

Footnotes

1. PBRT V4 9.3.4 Snell’s Law ↩ ↩²