Question

A point source of light is submerged 2.9 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have? Take the refraction index of water to be 1.333.

Answer 1

Answer:

The maximum radius of the circle is 3.288 m.

Explanation:

Given that,

Refraction index = 1.333

Distance = 2.9 m

We need to calculate the critical angle

Using formula of critical angle

$\sin\theta=\dfrac{1}{n}$

Put the value into the formula

$\sin\theta=\dfrac{1}{1.333}$

$\theta=\sin^{-1}(0.750)$

$\theta=48.59^{\circ}$

We need to calculate the maximum radius of the circle

Using formula of radius

$r=d\tan\theta_{c}$

Put the value into the formula

$r=2.9\times\tan(48.59)$

$r=3.288\ m$

Hence, The maximum radius of the circle is 3.288 m.