Question

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 $N / 100$, where $N$ is an integer, the value of $N$ is________.

Answer 1

$\tan r =\frac{15}{30}=\frac{1}{2}$
$\sin r =\frac{1}{\sqrt{5}}$
$1 \sin 45^{\circ}=\mu \sin r$
$\frac{1}{\sqrt{2}}=\mu\left(\frac{1}{\sqrt{5}}\right)$
$\mu=\sqrt{\frac{5}{2}}=1.581$
$\frac{ N }{100}=\mu$
$N =100 \mu$
$N =158.11$
So integer value of $N =158$