Question

A point source of light is placed $4 \,m$ below the surface of water of refractive index $\frac{5}{3}$. The minimum diameter of a disc, which should be placed over the source, on the surface of water to cut-off all right coming out of water is

• A. infinite
• B. 6 m
• C. 4 m
• D. 3 m

Answer 1

Answer: (B)

6 m

Answer 2

Light from the source goes in all directions, forming an angle of incidence to the surface of water. For angles greater than a critical angle, the light rays reflect back into the water. The critical angle $=\theta_{c}=\sin ^{-1} \frac{1}{\mu}=\sin ^{-1} \frac{3}{5}$ Thus, the radius of the disc required $= h \times \tan \theta_{ c }=4 \times \frac{3}{4} m =3\, m$ Hence, the diameter of the disc $=6 \,m$