A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $4 / 3$ and the fish is $12 \mathrm{~cm}$ below the surface, the radius of this circle (in $\mathrm{cm}$ ) is

• A

  $36 \sqrt{5}$
• B

  $4 \sqrt{5}$
• C

  $36 \sqrt{7}$
• Correct answer
  D

  $36 / \sqrt{7}$

Solution

$\sin i_{c}=\frac{1}{\mu}=\frac{r}{\sqrt{r^{2}+h^{2}}}$ Using $h=12 \mathrm{~cm}, \mu=4 / 3$
We get $\mathrm{r}=\frac{36}{\sqrt{7}} \mathrm{~cm}$

Hence, the correct answer is option: 'D'.