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37.   A hunter who is a bit of a braggart claims that from a
distance of 1.6 km he can selectively shoot either of two squirrels who are
sitting ten centimeters apart on the same branch of a tree. What’s more, he
claims that he can do this without the aid of a telescopic sight on his
rifle. (a) Determine the
diameter of the pupils of his eyes that would be required for him to be able
to resolve the squirrels as separate objects. In this calculation
use a wavelength of 498 nm (in vacuum) for the light. (b) State whether his claim is reasonable, and
provide a reason for your answer. In evaluating his claim, consider that the
human eye automatically adjusts the diameter of its pupil over a typical
range of 2 to 8 mm, the larger values coming into play as the lighting
becomes darker. Note also that under dark conditions, the eye is most
sensitive to a wavelength of 498 nm.
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