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Rumor has it that the U.S. military has spy satellites in orbit carrying telesco

ID: 1973910 • Letter: R

Question

Rumor has it that the U.S. military has spy satellites in orbit carrying telescopes that can resolve objects on the ground as small as the width of a car's license plate.

If we assume that such satellites orbit about 400 km above the ground (which is typical for orbiting telescopes) and that they focus light of wavelength 500 nm, what would have to be the minimum diameter of the mirror (or objective lens) of this kind of a telescope in order to resolve such small objects? Take the width of a typical license plate to be about 30.0 cm.

The answer in the back of the book is 81.3 cm, but I can't figure out how to get the answer. Do we use 1.22(/D)? Thanks!

Explanation / Answer

1.22 lambda / D = theta Rayleigh's criterion circular aperature d = R * theta R = distance and d = .3 m D = 1.22 * lambda * R / d combining equations D = 1.22 * 5 * 10E-7 * 4 * 10E5 / .3 = .813 m