Satellites used to map the earth photographically are typically about 100 miles

Question

Satellites used to map the earth photographically are typically about 100 miles (160 kilometers) above the surface of the earth, where there is almost no atmosphere to affect the orbit. If the lens in a satellite camera has a diameter of 18 cm, roughly how far apart do two objects on the earth's surface have to be in order that they can be resolved into two objects, if the resolution is limited mainly by diffraction? The key point is that the angle subtended by the two objects should be comparable to or bigger than the spread in angle 2?? introduced by diffraction of light going through the lens. Visible light has wavelengths from 400 to 700 nm; consider a wavelength somewhere in the middle of the spectrum. You should find that the numbers on a car license plate would be too blurred to read.

___________meter?

Explanation / Answer

The distance of the satellite is L = 100 miles                                                      = 160 km (1000 m/1km)                                                      = 160000 m The diameter of the lens is d = 18 cm                                                  = 18 cm(1 m /100 cm)                                                  = 0.18 m The wavelength of the visible light is = 550 nm                                                                  = 550 nm (1 m/109 nm)                                                                  = 550*10-9 m According to the Rayleigh's criterian = 1.22/d The condition for the diffraction is = D/L Here D is the distance between the two light sources 1.22/d = D/L D = 1.22L/d     = 1.22(160000 m)(550*10-9 m)/(0.18 m)     = 0.596 m

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