Question

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

• A. sin $\theta >8/9$
• B. 2/3 < sin $\theta$ < 8/9
• C. sin $\theta$ < 2/3
• D. None of these

Answer 1

Answer: (A)

Let ${\theta }_c$ C. be the critical angle at face BC, then
$sin{\theta }_c=\frac{{\mu }_w}{{\mu }_g}=\frac{4/3}{3/2}=\frac{8}{9}$
Angle of incidence at face B C is i =$\theta$
Total internal reflection (TIR) will take place on this surface if,
$i>{\theta }_{c}or\theta >{\theta }_{c}orsin{\theta }_{c}orsin\theta >\frac{8}{9}$
$\therefore$ Correct option is (a).