Index of Refraction Calculator

Refractive index describes how quickly light travels through a material compared with its speed in vacuum. It is defined as the vacuum speed of light divided by the light speed in the medium. Vacuum has an index of exactly one, air is very close to one, water is about 1.33, and many common glasses range from roughly 1.5 to 1.9. Values depend on wavelength, temperature, composition, and sometimes direction within the material. When a ray crosses a boundary, its frequency remains constant but its speed and wavelength change. That change usually bends the ray. Snell's law relates the incident and refracted angles: the first index times the sine of the incident angle equals the second index times the sine of the refracted angle. Both angles must be measured from the normal, an imaginary line perpendicular to the interface, rather than from the surface itself. Light bends toward the normal when it enters a higher-index medium and away from the normal when it enters a lower-index medium. A special condition occurs when light travels from a higher index to a lower index. As the incident angle increases, the refracted ray approaches the boundary. At the critical angle, the calculated refracted angle is 90 degrees. Beyond that point Snell's law has no real transmitted angle and total internal reflection occurs. The critical angle is the inverse sine of the lower index divided by the higher index. It is not applicable when the first index is less than or equal to the second. Total internal reflection guides light through optical fibres, prisms, light pipes, and many sensing systems. Ideal treatment assumes a flat boundary, homogeneous isotropic media, and refractive indices appropriate for the light's wavelength. Real interfaces can also reflect part of the light below the critical angle, absorb energy, scatter from roughness, or produce polarization-dependent effects. The calculator identifies the geometric ray direction but does not calculate reflected intensity or Fresnel transmission. Use accurate material data and consistent wavelengths when comparing optical designs. This tool is well suited to physics exercises, laboratory setup, aquarium viewing, lens-system checks, and preliminary fibre-optic reasoning. For precision instruments, account for wavelength dispersion, thermal changes, coatings, and manufacturing tolerances.