A right angled prism is to be made by selecting a proper material and the angles A and B `(BleA), 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

At P, angle of incidence `i_A=A` and at Q, angle of incidence `i_B=B`

if TIR satisfies for the smaller angle of incidence than for larger angle of incidence is
automatically satisfied.
`BleA`
`:. i_Blei_A`
Maximum value of B can be `45^@`. Therefore, if condition of TIR is satisfied for `45^@,` then
condition of TIR will be satisfied for all value of `i_A and i_B.`
Thus, `45^@getheta_C or sin 45^@gesin theta_C`
or `1/sqrt2ge1/mu or mugesqrt2`
`:.` Minimum value of `mu` is `sqrt2`.
(b) For `mu=5/3, sin theta_C=1/mu=sin^-1((3)/(5))~~37^@`
If `B=30^@` and `A=60^@` or `i_A=60^@, i_Agttheta_C` but `i_Blttheta_C`
i.e. TIR will take place at A but not at B.