Prof. Marcia Grail, supervillain and superscientist, wishes to spy on her foes (

Question

Prof. Marcia Grail, supervillain and superscientist, wishes to spy on her foes (they'll all pay!) from orbit. She wishes to be able to resolve detail on order the size of the letters on a license plate (approx 5cm), in a wavelength of approximately 550 nm, from an orbit approximately 4.2 x 10^7 m above the surface of the Earth. If her resolution is limited only by diffraction, then what is the smallest aperture telescope that she can get away with? How would this change if the satellite was closer to the surface of the Earth? For a bonus point, why would she prefer the distance of 4.2 x 10^7 m?

Explanation / Answer

given minimum resolvable detail dx = 5 cm
lambda = 550 nm
d = 4.2*10^7 m

smallest aperture of telescope = D
then
the from reilighs criterion
D/d = 1.22*lambda/dx
hence
D = 1.22*d*lambda/dx = 563.64 m

hecne the telescope aperture has to be of the order of half a kilometer

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