Question

The radius of the light circle observed by a fish at a depth of $12m$ is (refractive index of water $=\frac{4}{3}$)

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

Answer 1

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

The radius of the light circle is given by,
$r=\frac{h}{\sqrt{{\mu }^2-1}}$ (Key concept)
So, $r=\frac{12}{\sqrt{{\left(\begin{array}{c}\frac{4}{3}\end{array}\right)}^2-1}}=\frac{12}{\sqrt{\frac{16}{9}-1}}=\frac{12}{\sqrt{\frac{7}{9}}}=\frac{12\times 3}{\sqrt{7}}=\frac{36}{\sqrt{7}}$