JEE PYQ: Ray Optics Question 32
Question 32 - 2019 (09 Jan Shift 2)
There is a small source of light at some depth below the surface of water (refractive index $= \frac{4}{3}$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly):
[Use the fact that surface area of a spherical cap of height $h$ and radius of curvature $r$ is $2\pi rh$]
(1) 21%
(2) 34%
(3) 17%
(4) 50%
Show Answer
Answer: (3)
Solution
Given, Refractive index, $\mu = \frac{4}{3}$ $\frac{4}{3}\sin\theta = 1\sin 90°$ $\Rightarrow \sin\theta = \frac{3}{4}$ $\cos\theta = \frac{\sqrt{7}}{4}$ Solid angle, $\Omega = 2\pi(1 - \cos\theta) = 2\pi(1 - \sqrt{7}/4)$ Fraction of energy transmitted $= \frac{2\pi(1 - \cos\theta)}{4\pi} = \frac{1 - \sqrt{7}/4}{2} = 0.17$ Percentage of light emerges out of surface $= 0.17 \times 100 = 17%$
BETA
