The Physics of Refraction

When a light ray crosses the boundary between two transparent media, its speed changes and the ray bends. Snell's law, named for the Dutch mathematician Willebrord Snellius, states that the product of the refractive index and the sine of the angle to the normal is conserved across the boundary: n₁·sin(θ₁) = n₂·sin(θ₂). The refractive index itself is the ratio of the speed of light in vacuum to its speed in the medium, so denser optical materials like glass and diamond slow light more and bend rays more sharply. This single equation explains lenses, prisms, fiber optics, rainbows, mirages, and the apparent displacement of objects seen through water.

The direction of bending depends on the index change. Entering a higher-index medium, the ray bends toward the normal — light going from air into water at 45° emerges at roughly 32°. Entering a lower-index medium, it bends away from the normal, and beyond the critical angle it cannot emerge at all. The critical angle, θc = sin⁻¹(n₂/n₁), exists only when light travels from a higher-index into a lower-index medium, and it is the principle behind fiber-optic cables, which trap light inside a glass core through repeated total internal reflection.

Using the Calculator

Choose any two common media — air, water, crown glass, acrylic, or diamond — or specify custom refractive indices, and enter the incident angle. The calculator applies Snell's law, reports the refracted angle in degrees, and automatically flags total internal reflection when the geometry makes refraction impossible, alongside the critical angle for your media pair. This makes it a practical reference for optics students verifying homework, engineers designing lenses and light pipes, and anyone curious about how light behaves at the boundary between materials.