Refractive Index Calculator

Refractive index is a dimensionless number that describes how much the speed of light is reduced as it passes through a medium compared with its speed in a vacuum. The formula is n equals c divided by v, where c is the speed of light in vacuum (approximately 2.998 times 10 to the power of 8 metres per second) and v is the phase velocity of light in the medium. Glass has a refractive index of about 1.5, meaning light travels at two-thirds of its vacuum speed inside it. Water is about 1.33. When light crosses the boundary between two media with different refractive indices, it bends according to Snell's law: n1 times sin(theta1) equals n2 times sin(theta2), where theta1 and theta2 are the angles of incidence and refraction measured from the normal to the surface. If light is moving from a denser medium to a less dense one and the angle of incidence exceeds the critical angle, total internal reflection occurs and no light escapes. The critical angle is theta_c equals arcsin(n2 divided by n1). This calculator has two modes: a refractive index mode that finds n from the speed of light in the medium, and a Snell's law mode that finds the angle of refraction given n1, n2 and the angle of incidence, along with the critical angle if n1 is greater than n2. It is used in optics, photonics, fibre-optic engineering, and secondary and university physics. The speed of light in vacuum used is exactly 2.99792458 times 10 to the power of 8 m/s.

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Speed of light in vacuum c = 2.998 x 10⁸ m/s. Angles are measured from the surface normal. Total internal reflection occurs when the angle of incidence exceeds the critical angle (denser to less dense only).