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592.


Problem 43.17 (RHK)


A coin lies at the bottom of a pool with depth d and index of refraction n; as shown in the figure. We have to show that light rays that are close to the normal appear to come from a point below the surface. This distance is called the apparent depth of the pool.

Solution:           Click For PDF Version

As shown in the figure, we view the coin from air close to the normal. Therefore, the angle of incidence is small and we use the small angle approximation

.

From Snell’s law we find the angle of refraction .

In the small angle approximation, we have

,

where n is the index of refraction of water with respect to air. As the depth of the pond is d, we note

This gives that