examples of total internal reflection

Total Internal Reflection

One of the qualities of any optically transparent material is the speed at which light travels within the material, i.e., it depends upon the refractive index n of the material. The index of refraction is merely the ratio of the speed of light c in vacuum to the speed of light v in that material.Expressed mathematically:
n=c /v
The boundary between two optical media,e.g. glass and air having different refractive indices can reflect or refract light rays. The amount and direction of reflection and refraction is determined by the amount of difference indices as well as the angle at which the rays strike the boundary. At some angle of incidence , the angle of refraction is equal to 90°when a ray of light is passing through glass to air. This angle of incidence is called the critical angle  θ_c. We are already familiar with Snell’s law
Equations,……………………………………………..
Let us now assume that the glass is formed into a long, round rod. We known that all the right rays striking the internal surface  of the glass at angles of incidence greater than 41.8° will escape from the glass. Ray 1 is injected into the rod so that it strikes the glass air boundary at an angle of incidence about 30°.