roblem 28.56 A spy camera is said to be able to read the numbers on a car\'s lic

Question

roblem 28.56

A spy camera is said to be able to read the numbers on a car's license plate.

Part A

If the numbers on the plate are 4.0cm apart, and the spy satellite is at an altitude of 140km , what must be the diameter of the camera's aperture? (Assume light with a wavelength of 510nm .)

Express your answer using two significant figures.

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roblem 28.56

A spy camera is said to be able to read the numbers on a car's license plate.

Part A

If the numbers on the plate are 4.0cm apart, and the spy satellite is at an altitude of 140km , what must be the diameter of the camera's aperture? (Assume light with a wavelength of 510nm .)

Express your answer using two significant figures.

SubmitMy AnswersGive Up

Explanation / Answer

As we know that

tan(theta) = y/h

Also as we know

theta = theta min = 1.22*lambda/D

= 1.22*(510*10^-9)/D

theta= (622.2*10^-9)/D

Therefore we get

tan((622.2*10^-9)/D) = y/h

tan((622.2*10^-9)/D) = 0.04/(140*10^3)

D = 2.1777 m

= 2.2 m in 2 significant figures

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