An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical.How far is the sun above the horizon? (n_water = 1.333)

Question

Quizplus · Accepted Answer

Let h be the height of the Sun above the horizon. Then, using trigonometry, we have:

tan(45.0°) = h/d
where d is the distance from the diver to the point directly below the Sun on the surface.

We can rearrange this equation to solve for h:

h = d tan(45.0°)

Now, we know that the refractive index of water (n) is 1.333. This means that light bends when it enters or exits the water, and the apparent depth of objects is different from their actual depth. In this case, the apparent depth (d') is related to the actual depth (d) by:

n = d/d'

Rearranging, we have:

d' = d/n = d/1.333

Substituting this into the equation for h, we get:

h = (d/1.333) tan(45.0°)

Plugging in the values, we get:

h = (d/1.333) x 1 = 0.75d

So the height of the Sun above the horizon is 0.75 times the distance from the diver to the point directly below the Sun on the surface. Therefore, we cannot determine the height of the Sun without knowing the distance d.

Thus, the best choice is A) 19.5° as it indicates that the answer cannot be determined from the given information.

An Underwater Scuba Diver Sees the Sun at an Apparent