Question

A fish look up through the water sees the outside world containing in a circular horizon. The radius of the circle is $12\sqrt{7}\text{cm}$. The depth of the fish from the water surface is
[Refractive index of water is $\frac{4}{3}$]

• A. $14\text{cm}$
• B. $21\text{cm}$
• C. $28\text{cm}$
• D. $35\text{cm}$

Answer 1

The correct option is C $28\text{cm}$

Given,

$R=12\sqrt{7}\text{cm};\mu =\frac{4}{3}$

From the circle of illuminance we get,

$R=\frac{h}{\sqrt{{\mu }^2-1}}$

$\Rightarrow h=R\sqrt{{\mu }^2-1}$

$h=12\sqrt{7}\sqrt{{\left(\frac{4}{3}\right)}^2-1}=12\sqrt{7}\times \frac{\sqrt{7}}{3}$

$\therefore h=4\times 7=28\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.