Question

An underwater scuba diver sees the Sun at an apparent angle of 47.5° 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.)

Answer 1

Answer:

actual elevation angle above horizontal = $90{\circ} - 64.232{\circ} = 25.768^{\circ}$

Given:

apparent angle = $47.5^{\circ}$

refractive index of water, $\mu _{w}$ = 1.333

Solution:

angle of incidence, $\angle i = 90{\circ} - 47.5{\circ} = 42.5^{\circ}$

refractive index of water, $\mu _{a}$ = 1

Using Snell's law:

$\mu _{a}sini = \mu _{w}sinr$

$sinr =  \mu _{w}sini = 1.333sin42.5^{\circ}$

$r =sin^{-1}0.90056 = 64.232^{\circ}$

angle of refraction, $\angle r = 64.232^{\circ}$

Now,

actual elevation angle above horizontal = $90{\circ} - 64.232{\circ} = 25.768^{\circ}$