An observer can see through a small hole on the side of a jar (radius $15 \mathrm{~cm}$ ) at a point at height of $15 \mathrm{~cm}$ from the bottom (see figure). The hole is at a height of $45 \mathrm{~cm}$. When the jar is filled with a liquid up to a height of $30 \mathrm{~cm}$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid $\mathrm{N} / 100$, where $\mathrm{N}$ is an integer, the value of $\mathrm{N}$ is__________.
$\tan \mathrm{r}=\frac{15}{30}=\frac{1}{2}$
$\sin r=\frac{1}{\sqrt{5}}$
$1 \sin 45^{\circ}=\mu \sin \mathrm{r}$
$\frac{1}{\sqrt{2}}=\mu\left(\frac{1}{\sqrt{5}}\right)$
$\mu=\sqrt{\frac{5}{2}}=1.581$
$\frac{\mathrm{N}}{100}=\mu$
$N=100 \mu$
$N=158.11$
So integer value of $\mathrm{N}=15800$
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