Ray Optics and Optical Instruments - Result Question 22
22. 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 light coming out of water is [1994]
(a) $\infty$
(b) $6 m$
(c) $4 m$
(d) $3 m$
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Answer:
Correct Answer: 22. (b)
Solution:
(b) $\sin C=\frac{1}{\mu}=\frac{1}{\frac{5}{3}}=\frac{3}{5} \Rightarrow$ So, $\tan C=\frac{3}{4}$
Now, $\tan C=\frac{r}{h} ; r=h \tan C=4 \times \frac{3}{4}=3 m$
Diameter of disc $=2 r=6 m$
Field of vision of a swimmer or fish,
Radius, $r=h \tan c=\frac{h}{\sqrt{\mu^{2}-1}}$
Area, $A=\pi r^{2}=\frac{\pi h^{2}}{(\mu^{2}-1)}$
