Question

A fish looking up through the water sees outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$ and the fish is $12\text{cm}$ below the surface. The radius of this circle in $\text{cm}$ is

• A. $36\sqrt{7}$
• B. $\frac{36}{\sqrt{7}}$
• C. $36\sqrt{5}$
• D. $4\sqrt{5}$

Answer 1

Step1: Given

Refractive index of water, $\mu =$ $\frac{4}{3}$,
$h=12\text{cm}$

Step 2: Calculation of radius

The ray after refraction grazes along the surface when incident at critical angle $\left(C\right)$,

$\mu =\frac{1}{\sin C}$

$\sin C=\frac{1}{\mu }$

$\sin C=\frac{3}{4}$
$\tan C=\frac{3}{\sqrt{7}}=\frac{r}{12}$


Radius of circle is $r=\frac{36}{\sqrt{7}}\text{cm}$

The correct option is B $\frac{36}{\sqrt{7}}$