JEE PYQ: Ray Optics Question 16
Question 16 - 2020 (03 Sep Shift 1)
An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is $N/100$, where $N$ is an integer, the value of $N$ is __________.
Show Answer
Answer: (158)
Solution
From figure, $\sin i = \frac{15}{\sqrt{15^2 + 30^2}}$ and $\sin r = \sin 45°$ From Snell’s law, $\mu \times \sin i = 1 \times \sin r$ $\Rightarrow \mu \times \frac{15}{\sqrt{15^2 + 30^2}} = 1 \times \sin 45° = \frac{1}{\sqrt{2}}$ $\therefore \mu = \frac{\frac{1}{\sqrt{2}}}{\frac{15}{\sqrt{1125}}} = 158 \times 10^{-2} = \frac{N}{100}$ Hence, value of $N = 158$.
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