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Problem 3 You are standing in the middle of a long stretch of road at night, and a vehicle is moving toward you. The vehicle is sufficiently far away that you are unable to tell whether it is a motorcycle or a car, purely based on whether or not the vehicle has a single headlight, or two. (a) Assuming that the diameter of your pupils is 5 mm, and the wavelength of the light is A = 550 nm, what is the angular resolution of your eye? (b) Take the standard distance between car headlights to be 115 cm. At what distance will you be able to determine whether the vehicle is a car or motorcycle? (c) The Keck Observatory has two telescopes, each of which has a 10 m diameter. What is the angular resolution of one of these telescopes? Again, assume the wavelength is 550 nm. (d) At what distance would one of the Keck telescopes be able to distinguish a car from a motorcycle? Compare this distance to the circumference of the Earth (RE = 6371 km). Again assume that the distance between car headlights is 115 cm