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:

n1 sin α = n2 sin β


Incident, reflected and refracted rays

Using Snell's law given above, we can solve for β to obtain
β = sin
-1(n1 sin α / n2)
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 αc corresponding to β = 90 is called the critical angle and is given by Snell's law as follows
n
1 sin αc = n2 sin 90
sin α
c = n2 / n1
α
c = sin-1(n2 / n1)
If light rays are incident on a surface separating two media of indices n
1 > n2, total internal reflection occurs if the angle of incidence α is greter than the critical angle αc.
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 n1 > n2 and also angle β can be calculated if n1 sin α / n2 ≤ 1

Refraction and Critical Angles Calculator

Enter the indices n1 and n2 and the angle of incidence α in degrees then press "Calculate Angles".

Refractive Index in Medium 1: n1 =
Refractive Index in Medium 2: n2 =
Angle of Incidence: α =
Decimal Places =
Angle of Refraction: α =
Critical Angle: αc =

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

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