Snell's Law Calculator

This calculator applies Snell's law to find the angle at which light bends when it passes from one medium into another, and detects total internal reflection. When light crosses a boundary between two transparent materials, such as from air into water or glass, it changes direction, an effect called refraction. This is why a straw looks bent in a glass of water and why lenses can focus light. Snell's law describes it precisely: the refractive index of the first medium times the sine of the angle of incidence equals the refractive index of the second times the sine of the angle of refraction. The refractive index measures how much a material slows light, with a vacuum at exactly 1, air very close to 1, water about 1.33 and typical glass around 1.5. This tool does the calculation for you. You enter the refractive index of each medium and the angle of incidence, measured from the perpendicular to the surface, and the calculator returns the angle of refraction. When light travels from a denser to a less dense medium, it also reports the critical angle, the angle of incidence beyond which light cannot escape and is instead completely reflected back, a phenomenon called total internal reflection that makes optical fibres and many optical devices work. The results update as you type. Use it for physics homework, for understanding lenses, prisms and fibre optics, or for any refraction problem. Light bends toward the perpendicular when entering a denser medium and away from it when entering a less dense one. When total internal reflection occurs, the calculator flags it, since no refracted ray exists in that case.

n1 sin(θ1) = n2 sin(θ2). Angles measured from the normal. The critical angle applies only when n1 > n2 (denser to less dense). Rounded for display.