To focus a camera on objects at different distances, the converging lens is move
ID: 2207461 • Letter: T
Question
To focus a camera on objects at different distances, the converging lens is moved toward or away from the film, so a sharp image always falls on the film. A camera with a telephoto lens (f = 190.0 mm) is to be focused on an object located first at a distance of 3.5 m and then at 47.0 m. Over what distance must the lens be movable?Explanation / Answer
U = object distance, V = image distance , f = focal length (1 / V ) + (1 / U) = 1 / f => 1 / V = (1 / f ) - (1 / U) = (U - f) / (U f) => V = (U f) / (U - f) .......... (1) f = 200 mm = 1/5 m = 0.2 m (1) U1 = 3.5 m, V1 = {(3.5) * (0.2)} / {3.5 - 0.2} = 0.7 / 3.3 = 0.212 m (2) U2 = 50 m, V2 = {(50) * (0.2)} / {50 - 0.2} = 10 / (49.8) = 0.201 m V2 - V1 = (0.201) - (0.212) = - 0.011 m = - 11 mm The negtive sign indicates that the lens is to be moved backwards by 11 mm