Question

A fish looking up through water sees the outside world contained in a circular horizon. If the fish is $12\text{cm}$ below the surface of water $(\mu =4/3)$, the radius of circle will be

• A. $\frac{16}{\sqrt{7}}\text{cm}$
• B. $\frac{26}{\sqrt{7}}\text{cm}$
• C. $\frac{36}{\sqrt{7}}\text{cm}$
• D. $\frac{46}{\sqrt{7}}\text{cm}$

Answer 1

The correct option is C $\frac{36}{\sqrt{7}}\text{cm}$

Given:
Depth of fish in water, $h=12\text{cm}$
Refractive index of water, $\mu =\frac{4}{3}$
So, the radius of the circle,
$r=\frac{h}{\sqrt{{\mu }^2-1}}$
$\Rightarrow r=\frac{12}{\sqrt{(4/3{)}^2-1}}=\frac{36}{\sqrt{7}}\text{cm}$

Why this question? Fish sees the outer world to be in a circular horizon due to the phenomenon of total internal reflection.