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?

Answer

B

Explanation

(i) Let x is the incident angle for reflection at AC. For total internal reflection`xgti_(C)` (critical angle)`
Let y be the incident angle of the ray on face CB. For total internal reflection
`ygti_(C)`
`:'``x+ygt2i_(C)`
But `x=angleA` and `y=angle B` ( from geometry)
`:'``x+y=90^circ`
`implies``90gt2i_(C)implieslt45^circ`
The refrective index of the medium for this to happen.
`mu=(1)/(sini_(C))=(1)/(sin45^circ)=sqrt2`
(ii) `mu=(5)/(3)` `impliessini_(C)=(1)/(mu)=(1)/((5)/(3))=(3)/(5)impliesi_(C^`)=37^circ` `y=30^circ`(given) `:'``x=60^circ`
`xgti_(C^(`))` But `ylti_(C^(`))` `implies` Total internal reflection will take place on face AC but not on CB.