Chapter 24, Problem 79GP

To determine

Angle of the Sun above the horizon.

Answer to Problem 79GP

Angle of the Sun above the horizon is $\alpha =36.94°$

Explanation of Solution

Given:

Refractive index of water, $n_w=1.33$

Refractive index of air, $n_a=1.00$

Formula used:

  $\tan {\theta }_p=\frac{n_w}{n_a}$

Here,

  ${\theta }_p$ is the angle of polarization.

  $n_w$ is the refractive index of water

  $n_a$ is the refractive index of air

Calculation:

Substituting all the values in the above formula, we get:

  $\begin{array}{l}{\theta }_p={\tan }^{-1}\left(\frac{n_w}{n_a}\right)\\ {\theta }_p={\tan }^{-1}\left(\frac{1.33}{1.00}\right)\\ {\theta }_p=53.06°\end{array}$

Now, the angle at which sun is reflected from water is given by:

  $\begin{array}{l}\alpha =90°-{\theta }_p\\ \alpha =90°-53.06°\\ \alpha =36.94°\end{array}$

Conclusion:

Thus, the angle of the Sun above the horizon is $\alpha =36.94°$