109 In Fig, 34-53, a fish watcher at point Pwatches a fish through a glass d wal

Question

109 In Fig, 34-53, a fish watcher at point Pwatches a fish through a glass d wall of a fish tank. The watcher is level with the fish; the index of re- ip fraction of the glass is R/5, and that of Watcher the water is 43. The distances are d1- 8.0 cm, d 3.0 cm, and d, m 6.8 cm. (a) To the fish, how far away does the watcher appear to b? Wall (FHint: The watcher is the objeci. Light from that object passes Fig. 34-53 Problem 109. through the wall's outside suržace, which acts as a refracting sur face. lind the image produced by that surface. Then treat that im age as an object whose light passes through the wall's inside sur- face, which acts as another refracting surface. Find the image produced by that surtace, and there is the answer.) (b) lo the n watcher, how far away does the fish appear to be?

Explanation / Answer

The light will pass straight through the water and the tank, at no angle.

The 'optical thickness' and the thickness are not the same. In fact, you could show that the optical thickness of an object is its thickness times its refractive index.

So to one, the other will appear to be a distance of 8.0 cm + 8*3.0 cm/5 + 4*6.8 cm/3
= 8.0 cm + 4.8 cm + 9.07 cm
= 21.87 cm.

And the same will be true the opposite way, meaning the answer to b is the same as the answer to a.

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