# Refraction and Critical Angles Calculator

A calculator that uses Snell's law to calculate the angle of refraction and the critical angle for total internal reflection is presented.

One of the most important parameters that measures optical properties of a medium is the index of refraction (or refractive index). When light rays are incident on a surface separating two media of different indices, there is
reflection and refraction of light as shown in the diagram below and Snell's law gives a relationship between the angle of incidence α and angle of refraction β as follows:

n_{1} sin α = n_{2} sin β

Using Snell's law given above, we can solve for β to obtain

β = sin^{-1}(n_{1} sin α / n_{2})

In many applications, we need total internal reflection of light within medium (1). Optical fibers are examples of systems where total internal reflection of light is used to carry light between distant points.
The angle of incidence α_{c} corresponding to β = 90 ° is called the critical angle and is given by Snell's law as follows

n_{1} sin α_{c} = n_{2} sin 90°

sin α_{c} = n_{2} / n_{1}

α_{c} = sin^{-1}(n_{2} / n_{1})

If light rays are incident on a surface separating two media of indices n_{1} > n_{2}, total internal reflection occurs if the angle of incidence α is greter than the critical angle α_{c}.

This calculator computes the angle of refraction β using Snell's law and the critical angle α_{c} given above.

NOTE that the critical angle α_{c} exixts only if n_{1} > n_{2} and also angle β can be calculated if n_{1} sin α / n_{2} ≤ 1

## Refraction and Critical Angles Calculator

Enter the indices n_{1} and n_{2} and the angle of incidence α in degrees then press "Calculate Angles".

## More References and Links

Total Internal Reflection of Light Rays at an Interface, Examples and Solutions.

Refraction of Light Rays, Examples and Solutions

Optical Fibers