(a) Fig. shows a cross-section of a 'light pipe' made of a glass fibre of refractive index `1.68`. The outer covering of the pipe is made of a material of refractive index `1.44`. What is the axis of the pipe for which total reflection inside the pipe take place as shwon.
(b) What is the answer if there is no outer covering if the pipe ?

Explanation

We know that maximum launching angle in case of optical fibre as `i_(raM)= sin^(-1) (sqrt(mu_(2)^(2) -mu_(1)^(2)))`
`i_(max) = sin^(-1) (sqrt( (1.68)^(2)- 1.44^(2)))`
`i_(max) = sin^(-1) (0.8653) = 59^(0)55^(1)`
This is the maximum value of i. All light rays with angle of incidence between `o^(@)` and `59^(0)55^(1)` will undergo total internal reflection.