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  4. A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is (4/3), and the diver's eyes are 15 cm below the surface of water. Then the radius of the circle is :

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Q. A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$, and the diver's eyes are $15\, cm$ below the surface of water. Then the radius of the circle is :

JEE MainJEE Main 2014Ray Optics and Optical Instruments

Solution:

$\sin\,\theta_{C}=\frac{1}{4/ 3}=\frac{3}{4}$
$\tan\,\theta _{C}=\frac{3}{\sqrt{7}}=\frac{r}{h}$
$r=\frac{3}{\sqrt{7}}\times15$

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