Question

The radius of the light circle observed by a fish at a depth of $12$ meter is (refractive index of water = $4/3$)

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

Answer 1

Answer: (B)

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