Question

Sunlight passes into a raindrop at an angle of 22.5° from the normal at one point on the droplet.What is the angle of refraction if the index of water is 1.333?Sketch a drawing to illustrate the path of the light ray.

Answer 1

We are asked to determine the angle of refraction of sunlight when passing through a raindrop. To do that we will use Snell's law:

$n_1\sin\theta_1=n_2\sin\theta_2$

Where:

$\begin{gathered} n_1,n_2=\text{ index of refraction of air and water} \\ \theta_1,\theta_2=\text{ angle of incidence and refraction} \end{gathered}$

The index of refraction of air is 1 and the index of refraction of water is 1.333. Now, we substitute the values:

$(1)\sin(22.5)=1.333\sin(\theta_2)$

Now, we divide both sides by 1.333:

$\frac{\sin(22.5)}{1.333}=\sin\theta_2$

Solving the operations we get:

$0.287=\sin\theta_2$

Now, we take the inverse function of sine, and we get:

$\sin^{-1}(0.287)=\theta_2$

Now, we solve the operation:

$16.68=\theta_2$

Therefore, the angle of refraction is 16.68°.

A diagram of the situation is the following: