Snell's Law

Snell’s Law is a Law of Geometric Optics that describes the behavior of light’s refraction through materials. Snell’s Law is as follows: $n_i\sin {\theta }_i=n_t\sin {\theta }_t$ where n is the index of refraction (see below) for the respective material.

The Index of Refraction

The index of refraction is a critical material quantity that is derived from Maxwell’s Equations. It gives the degree to which light is refracted through a material. This quantity is equal to: $n=\frac{c}{v}$ where c is the speed of light in a vacuum, and v is the speed of light in the material.

NOTE: THE INDEX OF REFRACTION DOES VARY FOR DIFFERENT WAVELENGTHS OF LIGHT IN VARIOUS MATERIALS. A TABLE IS SHOW BELOW

The Critical Angle.

When the transmitted angle is 90 degrees, we say that this is the critical angle. This is because the equation becomes: $\sin {\theta }_i=\frac{n_t}{n_i}$ This critical angle has another special property. If the light passes through a medium to another medium at the critical angle, no light will go into the second medium. The critical angle is given by: $\theta ={\sin }^{-1}(\frac{n_t}{n_i})$

Total Internal Reflection

This is another subcase of Snell’s law. When the angle of refraction is greater than the incident angle ($n_i$ must be greater than $n_t$), we say that there’s total internal reflection.

This property has an incredibly important property. If the light is kept inside the medium and reflected internally only, the light will lose no energy. This means that the light can travel for much greater distances than otherwise. This is the principle by which fiber optic cables work.