5. Total Internal reflection

We saw that when a ray of light enters an optically denser medium, it bends towards the normal.  Conversely, when the ray enters an optically rarer medium it bends away from the normal. 

When the ray is going from denser medium to rarer medium, according to the definition of refractive index,

sin i/sin r = 1 / μ .                                             Eq. 5

Note that

glass μ air    =   1/ air μ glass   =  1 / μ ,                Eq. 6   

In the following figures, the source is at S within the medium. As the angle of incidence increases, the angle of emergence increases according to Equation 5. 

In the case of glass, μ =1.52. 

Let us see for what value of i, r  becomes 90 Deg; from Eq. 5,

ic   = sin-1 (sin 90 / 1.52)

  = 41.1 Deg.

For a given medium ic   is called as the critical angle.

When i > ic , the refraction in the air is no longer possible and the light is totally reflected.

As we saw in the beginning, the ray of light gets partially reflected and partially refracted.  Although not shown in these figures,  the ray SO always has a reflected component though small. When the ray undergoes total internal reflection, all the energy is reflected.

The phenomenon of total internal reflection of light has wide applications. In optical instruments for example in binoculars, the length of the instrument is reduced by bending the rays using total internal reflection with the help of right angled prisms.  Optical fibers are used widely in the modern era; the ray propagates in the fiber undergoing multiple total internal reflections at the inner surface of the fiber.