You look down at a coin that lies at the bottom of a pool of liquid of depth d a

Question

You look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (In the Figure). Because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to be where extensions of the intercepted rays cross, at depth da instead of d. Assuming that the intercepted rays in in the Figure are close to a vertical axis through the coin, show that da = d/n. (Hint: Use the small-angle approximation sin Theta approx tan Theta approx Theta.)

Explanation / Answer

Sin i/Sin r=1/n

Tan i/Tan r=1/n

Let x be the horizontal displacement of the ray from the bottom of the pool to the surface.

(x/d)/(x/da)=1/n

da/d=1/n

da=d/n

Hence proved.

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