Question

A fish looking from within water sees the outside world through a circular horizon. If the fish is $\sqrt{7} m$ below the surface of water, what will be the radius of the circular horizon ?

• A. $3 m$
• B. $\frac{3}{\sqrt{7}} m$
• C. $\sqrt{7} m$
• D. $3 \sqrt{7} \,m$

Answer 1

Answer: (A)

Refractive index of water, $ \mu=4 / 3$

$\sin C=\frac{1}{\mu}=\frac{3}{4}$
$\tan C=\frac{3}{\sqrt{7}}\,\,\,\,\dots(i)$
From figure
$\tan C=\frac{A D}{O D}=\frac{r}{\sqrt{7}}\,\,\,\,\dots(ii)$
From equations (i) and (ii), we get
$r =3 m$