Snell's Law Calculator

Snell's law describes how a ray changes direction when it crosses a boundary between transparent media. It states that the first refractive index multiplied by the sine of the incident angle equals the second refractive index multiplied by the sine of the refracted angle. Both angles are measured from the normal, an imaginary line perpendicular to the boundary, rather than from the surface itself. Refractive index is the ratio of light speed in vacuum to light speed in a material. Vacuum has an index of exactly one, air is very close to one, water is about 1.333 in visible light, and common glass is often near 1.5. The precise value depends on wavelength, temperature, composition, and material structure. For accurate optical design, use index data for the actual material and wavelength instead of a generic rounded value. When light enters a medium with a higher refractive index, it bends toward the normal, so the refracted angle is smaller than the incident angle. When it enters a lower-index medium, it bends away from the normal. The calculator rearranges Snell's law to solve for the second angle: take the inverse sine of the first index times the sine of the incident angle divided by the second index. Angles are converted between degrees and radians for JavaScript's trigonometric functions. If light travels from a higher-index medium toward a lower-index medium, the requested sine of the refracted angle can exceed one. No real transmitted angle then satisfies Snell's law, and total internal reflection occurs. The threshold incident angle is called the critical angle. Above it, an ideal interface reflects the ray back into the first medium. Fiber-optic cables, prisms, and many optical sensors make practical use of this effect. The ray model assumes a flat boundary, homogeneous isotropic media, and a well-defined wavelength. It does not calculate reflected intensity, polarization, absorption, scattering, surface roughness, or multilayer interference. Near a real interface, a small evanescent field can extend into the second medium during total internal reflection. Wave optics or Fresnel equations are needed when amplitude, phase, and polarization matter. Use this calculator for classroom optics, aquarium viewing estimates, prism reasoning, lens-system checks, and quick refraction comparisons. Enter positive refractive indices and an incident angle from zero up to but not including ninety degrees. A zero-degree ray follows the normal and does not bend. Always confirm whether a published angle is measured from the normal or from the surface, because confusing these conventions changes the answer substantially.