Question

An observer can see through a small hole on the side of a jar $($radius $15\text{cm})$ at a point at height of $15\text{cm}$ from the bottom (see figure). The hole is at a height of $45\text{cm}.$ When the jar is filled with a liquid up to a height of $30\text{cm}$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is $\frac{N}{100}$ where $N$ is an integer. The value of $N$ is ____.

Answer 1

From figure, $\sin i=\frac{15}{\sqrt{{15}^2+{30}^2}}$ and $\sin r=\sin {45}^{\circ }$

From Snell's law, $\mu \times \sin i=1\times \sin r$

$\Rightarrow \mu \times \frac{15}{\sqrt{{15}^2+{30}^2}}=1\times \sin {45}^{\circ }=\frac{1}{\sqrt{2}}$

$\therefore \mu =\frac{\frac{1}{\sqrt{2}}}{\frac{15}{\sqrt{1125}}}=\frac{\sqrt{5}}{\sqrt{2}}=158\times {10}^{-2}=\frac{N}{100}$

Hence, value of $N\simeq 158$