(a) For a ray of light travelling from a denser medium of refractive index `n_(1)` to a rarer medium of refractive index `n_(2)`, prove that `(n_(2))/(n_(1)) = sin i_(c)`, where `i_(c)` is the critical angle of incidence for the media.
(b) Explain with the help of a diagram, how the above principle is used for transmission of video signals using optical fibers.

Explanation

(a) When `i=i_(c), " " r=90^(@)`
Using snell's law of refraction :
`n_(1) sin i_(c)= n_(2) sin 90^(@)`
`sin i_(c)=(n_(2))/(n_(1))`
`:. i_(c)=sin^(-1) ((n_(2))/(n_(1))) ` where [ `i_(c)` is critical angle i.e. the angle of incident in the denser medium for which angle of refraction in the rarer medium is `90^(@)`.
(b) When a video signal is directed into an optical fibre at a suitable angle, it undergoes internal reflections repeatedly along the length of the optical fibre and comes out of it with almost neglible loss of intensity.