Question

A diver at a depth of 12m in water (n=4/3) sees the sky in a cone.Find the semi vertical angle

Answer 1

Answer:

The semi-vertical angle is $\sin^{-1}\frac{3}{4}$

Step-by-step explanation:

Given the refractive index of water w.r.t. air

$n_{w/a}=\frac{4}{3}$

Thus refractive index of air w.r.t. the water

$n_{a/w}=\frac{1}{n_{w/a}}=\frac{3}{4}$

Let the incidence angle in water be $i$

Then the angle of refraction in air $r=90^\circ$

From Snell's Law we know that

$n_{a/w}=\frac{\sin i}{\sin r}$

$\implies n_{a/w}=\frac{\sin i}{\sin 90^\circ}$

$\implies \frac{3}{4}=\sin i$

$\implies i=\sin^{-1}\frac{3}{4}$

Hope this answer is helpful.