question_answer

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

A)  infinite                                

B)  6 m

C)  4m                        

D)         3m

Correct Answer: B

Solution :

Let\[S\]be the light source. If light falls on the surface at critical angle\[C\], it grazes along the surface as shown.                 \[\sin C=\frac{1}{n}=\frac{3}{5}\] From\[\Delta QSR\], we have                 \[\tan C=\frac{QR}{QS}=\frac{r}{4}\] \[\Rightarrow \]               \[\frac{3}{4}=\frac{r}{4}\] \[\Rightarrow \]               \[r=3\] Hence, diameter\[=2r=2\times 3=6\,\,m\]