A screen is located at a distance of 40 cm from an illuminated object. A converging lens is placed between the object and the screen in an attempt to form an image of the object on the screen. If no such position can be found, the focal length of the lens

Step-by-step solution

Let the distance between the object and the screen be D , and the object distance from the lens be x . The image distance from the lens is D - x . Using the lens formula, 1 v - 1 u = 1 f 1 D-x - 1 -x = 1 f x + D - x x(D-x) = 1 f x^2 - Dx + Df = 0 For a real position of the lens to exist, the roots of this quadratic equation must be real, which requires the discriminant to be greater than or equal to zero: D^2 - 4Df 0 D 4f Since no such position can be found, the roots must be imaginary, which means: D Given D = 40