🌈Snell's Law Calculator

About this tool

Choose the two materials (or type refractive indices) and the angle of incidence. The tool gives the refracted angle or flags total internal reflection, plus the critical angle, Brewster's angle, the fraction of light reflected and the speed of light in the second material.

Refraction and total internal reflection

Light slows down in transparent materials by a factor called the refractive index n: about 1.33 for water, 1.5 for glass and 2.42 for diamond. Crossing a boundary at an angle, it bends according to Snell's law, n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal. Light going from air into water at 45° continues at 32°, which is why a pool looks shallower than it is. Going from a higher to a lower index, rays bend away from the normal, and beyond the critical angle, arcsin(n₂ ÷ n₁), they can't escape at all: total internal reflection. That's 48.6° from water to air, 41.1° from glass and just 24.4° from diamond, which is why diamonds sparkle and how optical fibres carry light. At Brewster's angle, arctan(n₂ ÷ n₁), reflected light is completely polarised, which is why polarising sunglasses cut glare. The reflectance comes from the Fresnel equations: about 4% at normal incidence on glass. Honest limits: refractive index varies with wavelength (dispersion), and the presets are typical values for yellow light. The lens equation calculator and the wavelength and frequency calculator are related.

Frequently asked questions