A spy satellite uses a telescope with a 2.3-m-diameter mirror. It orbits the ear

Question

A spy satellite uses a telescope with a 2.3-m-diameter mirror. It orbits the earth at a height of 190 km .

Part A

What minimum spacing must there be between two objects on the earth's surface if they are to be resolved as distinct objects by this telescope? Assume the telescope's resolution is limited only by diffraction and that it is recording light with a wavelength of 500 nm.

A spy satellite uses a telescope with a 2.3-m-diameter mirror. It orbits the earth at a height of 190 km .

Part A

What minimum spacing must there be between two objects on the earth's surface if they are to be resolved as distinct objects by this telescope? Assume the telescope's resolution is limited only by diffraction and that it is recording light with a wavelength of 500 nm.

Explanation / Answer

Solution, ;-

Given data ,

d = 2.3 m , h = 190 km , lamda = 500 nm

sin(theta) = 1.22*lamda/d

sin(theta) = 1.22*500*10^-9/2.3

sin(theta) = 2.65*10^-7

Rays from the two objects on Earth's surface have the same angular separation as they enter the telescope

sin(theta) = object seperation/distance from telescope

2.65*10^-7 = x/(190*1000)

x = 5.0 cm

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