Snell's Law Calculator

This is an online calculator that calculates the angle of refraction using Snell's Law. Just enter the angle of incidence, refractive indices of the incident and refracting medium to get the corresponding angle of refraction value.
Enter the Angle of Incidence, Refractive Index of Incident Medium, and Refractive Index of Refracting Medium to Calculate the Angle of Refraction Value
  • Degrees

Result

  • Angle of Refraction
    Degrees
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Snell’s law, also known as the law of refraction gives the relation between the angle of incidence, the angle of refraction and the refractive indices of a given pair of media. We know that when light travels from one medium to another medium with a varying refractive index, it experiences refraction or bending. This degree of bending or the angle of refraction is given by Snell’s law. The formula is given by,



Here θ1 and θ2 are the angle of incidence and angle of refraction respectively. n1 and n2 are the refractive indices of the two medias.


Consider a ray of light travelling from point P to Q which are the points in medias with refractive indices n1 and n2 respectively. The time required to travel between these points can be calculated as the distance between the two points divided by the phase velocity. Phase velocity is the velocity of light in that medium. The time, T is given by,


Here a, b, l and x are denoted in the figure. v1 and v2 are the phase velocities of medium 1 and 2 respectively and is given by,


Here c is the speed of light in vacuum.

According to Fermat’s principle, light travels in the shortest path which has the least travelling time. So, the value of T given above is always the minimum. So we can write,


From the figure, 


So, (2) becomes,


Now substituting for v1 and v2 from (1), we get,


From here we get the equation for the angle of refraction θ2 as,