Total Internal Reflection

Total internal reflection is an optical phenomenon that happens when a ray of light strikes a
medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary, no light can
pass through and all of the light is reflected. The critical angle is the angle of incidence above
 which the total internal reflection occurs.

 

When light crosses a boundary between materials with different refractive induces, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the
critical angle – the angle of incidence at which light is refracted such that it travels along the
boundary – then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher
[n1=higher refractive index] to one with a lower refractive index [n2=lower refractive index].
For example, it will occur when passing from glass to air, but not when passing from air to glass.


Critical Angle






                     The critical angle is the angle of incidence above which total internal reflection occurs.The angle of incidence is measured with respect to the normal at the refractive boundary.
The critical angle θ_c is given by:

where n2 is the refractive index of the less optically dense medium, and n1 is the refractive
 index of the more optically dense medium.

The derivation for this is simple, and can easily be demonstrated using Snell's Law:

Rearranging Snell's Law, we get sin θr = (n1/n2)sin θi .
To find the critical angle, we find a value for θi such that the left hand side of this
equation equals 1. The resulting value of θi is equal to the critical angle θc.