A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3)…

Q: A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach the face BC if
Ray Optics

(A) sin θ > 8/9

(B) 2/3 < sin θ < 8/9

(C) sin θ < 2/3

(D) None of these

Ans: (A)

Sol: Let θc be the critical angle at face AC

$\large sin\theta_c = \frac{\mu_w}{\mu_g}$

$\large sin\theta_c = \frac{4/3}{3/2} = \frac{8}{9}$

Here , Angle of incidence at face AC is i = θ (from geometry)

For TIR on this surface , θ > θc

$\large sin\theta > sin\theta_c $

$\large sin\theta > \frac{8}{9} $