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34.  It is claimed that some
professional baseball players can see which way the ball is spinning as it
travels toward home plate. One way to judge this claim is to estimate the
distance at which a batter can first hope to resolve two points on opposite
sides of a baseball, which has a diameter of 0.0738 m. (a) Estimate this distance,
assuming that the pupil of the eye has a diameter of 2.0 mm and the
wavelength of the light is 550 nm in vacuum.
(b) Considering that the distance between
the pitcher’s mound and home plate is 18.4 m, can you rule out the claim
based on your answer to part (a)?
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As the distance away
decreases, the angle subtended increases.
This means if someone is observing the two spots closer than this
distance, they will be able to resolve the two spots at least from
diffraction conditions. Since 220 m
>> 18.4 m, clearly the claim cannot be ruled out!
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