Question

An underwater scuba diver sees the Sun at an apparent angle of 43.0° above the horizontal. What is the actual elevation angle of the Sun above the horizontal? (Use 1.333 for the index of refraction of water.) e above the horizon

Answer 1

Answer:

The actual elevation angle is 12.87 degrees

Explanation:

In the attachment you can clearly see the situation. The angle of elevation as seen for the scuba diver is shown in magenta, we conclude that $\theta_2=90-43=47$.

Using Snell's Law we can write:

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

$\implies \sin(\theta_1)=\frac{n_2}{n_1}\sin(\theta_2)$,

Let's approximate the index of refraction of the air (medium 1 in the picture) to 1.

We thus have:

$\sin(\theta_1)=n_2\sin(\theta_2)=1.333\sin(47)$

$\implies\theta_1=\arcsin[n_2\sin(\theta_2)]=\arcsin[1.333\sin(47)]\approx 77.13$. Calling $\alpha$ the actual angle of elevation, we get from the picture that $\alpha=90-77.13=12.97$