Show that for a material with refractive index `mu ge sqrt(2)`, light incident at any angle shall be guided along a length perpendicular to the incident face.

Explanation

In Fig, we have shown a ray of light incident at `/_i` on face `AB`. It is refracted at `/_r` and falls on face `AD _|_ AC` at `/_ phi`. This ray will suffer total internal reflection at `K` and proceed along `KD_|_ AB`, provided.
`sin phi ge (1)/(mu)`
`sin (90^@ - r) ge (1)/(mu)` or `cos r ge (1)/(mu)`
or `1 - cos^2 r le 1 - (1)/(mu^2)` or `sin^2 r le 1 - (1)/(mu_2)`
According to Snell's law, `sin i = mu sin r :. (1)/(mu^2) sin^2 i le 1 - (1)/(mu^2)`
`sin^2 i le mu^2 - 1`
`phi` will be smallest when `i ~~ 90^@`
`sin^2 i = sin^2 90^@ = 1 :. 1 le mu^2 - 1` or `mu^2 ge 2` or `mu ge sqrt(2)`, which was to be proved.
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