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You look down at a coin that lies at the bottom of a pool
Chapter , Problem 112(choose chapter or problem)
You look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (Fig. 34-57). 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 Fig. 34-57 are close to a vertical axis through the coin, show that da ! d/n. (Hint: Use the small-angle approximation sin u % tan u % u.)
Questions & Answers
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 (Fig. 34-57). 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 Fig. 34-57 are close to a vertical axis through the coin, show that da ! d/n. (Hint: Use the small-angle approximation sin u % tan u % u.)
ANSWER:Problem 112
You look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (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 instead of d. Assuming that the intercepted rays in figure are close to a vertical axis through the coin, show that
(Hint: Use the small-angle approximation )
Step By Step Solution
Step 1 of 3
Let’s consider water as medium ,so ,and the air is medium , for which .
Now we can refer to points where the light rays strike the water surface as (which is on the left side of the figure) and (which is on the right side of the figure). The point midway between and is (the center point).
The penny is directly below , and the position of the apparent or virtual penny is .