Remote sensing satellites move in an orbit that is at an average height of about 500   k m from the surface of the earth. The camera onboard one such satellite has a screen of area A on which the images captured by it are formed. If the focal length of the camera lens is 50   c m , then the terrestrial area that can be observed from the satellite is close to

Step-by-step solution

Consider the given diagram, Assuming area observed and screen both circular, we have θ 1 = θ 2 ⇒ d 1 f = d 2 h ⇒ d 2 d 1 = h f where, d 1 = diameter of camera screen and d 2 = diameter of area on earth. Now, area observed on earth area of screen = A 0 A = π · d 2 2 4 π · d 1 2 4 = d 2 2 d 1 2 ⇒ A 0 A = h f 1 2 = 500 × 10 + 3 50 × 10 - 2 2 = 10 × 10 3 × 10 2 2 = 10 6 2 = 10 12