A right angled prism is to be made by selecting a proper material and the angles A and B `(B <= A), as shown in figure. It is desired that a ray of light incident on the face AB emerges parallel to the incident direction after two internal reflections.

(a) What should be the minimum refractive index n for this to be possible?
(b) For `n=5/3` is it possible to achieve this with the angle B equal to `30` degrees?

Explanation

(`a`) As already discussed
`Agetheta_(c )`, `Bgetheta_(c )` Also `BleA`
Case : `1 : B=A=pi//4rArrtheta_(c )lepi//4`…..(`1`)
Case `2 : B lt A`. Hence, for reflection at both faces
`B gt theta_(c )`
But, `B lt pi//4rArrtheta_(c ) lt pi//4` (as `2B lt pi//2`).......(`2`)
Combining Eqs. (`1`) and (`2`), we get `theta_(c ) le pi//4`
`(1)/(n) le(1)/(sqrt(2))rArrn ge sqrt(2)`
`n_(min)=sqrt(2)`
(`b`) This pertains to case (`2`)
Hence, `theta_(c ) lt 30^(@)` But `theta_(c )=sin^(-1)(3//5)` which is more than `30^(@)` and hence, it is not possible.