A ray of light enters a diamond (n=2) from air and is being internally reflected near the bottom as shown in the figure . Find the maximum value of angle `theta` possible.

Answer

`sin^(-)((sqrt(3)-1)/(sqrt(2)))`

Explanation

`90 - x - 360^(@) - [135 + 90 + 90-r] implies x = 45-r`

For totally internal reflection
2 sin (45-r) = 1 sin `90^(@)`
`implies "sin"(45-r) "sin"30^(@) implies r = 15 ^(@)`
from snell's law `1 "sin"theta = 2 "sin"15^(@)`
`implies "sin v" = 2 xx (sqrt(3) - 1)/(2sqrt(2)) implies theta = sin^(-1) ((sqrt(3)-1)/(sqrt(2)))`