Chapter 23, Problem 9Q

To determine

(a) To analyze:

That the depth of the swimming pool or a lake is overestimated or underestimated, when it is looked down.

Answer to Problem 9Q

Solution:

When you look down into a lake or pool, you will underestimate its depth.

Explanation of Solution

The ray diagram below shows the depth of the swimming pool.

Two rays going upward from a point on the rock incident at the water surface at a small angle as shown by 1

The rays are being refracted away at the water’s (flat)surface from the normal as they exit the water. (Depicted in 2)

The refracted rays reach the eyes (as in 3)

The eyes see the image that appears to be diverging from apoint above the rock (dashed lines), which is why the water seems less deepthan it actually is. (as in 4)

To determine

(b) To determine:

The apparent depth of the swimming pool or lake vary with the viewing angle

Answer to Problem 9Q

Solution:

As the viewing angle gets larger (when the angle of refraction increases), the pool appears to get more shallow.

Explanation of Solution

The rock under the swimming pool water is looking down at different angles.

If the rock is looking down at the large viewing angle (the angle of refraction increases)

The rock at the bottom of the pool is viewed from nearly straight above,

The rock appears to be placed deeper if the rock is viewed as in figure.