A convex lens forms a real image of an object on a fixed screen. The distance between the object and the screen is 90 cm . The focal length of the lens is 20 cm . If the lens is placed such that the image formed on the screen is magnified, the distance of the object from the lens is ________ cm .

Step-by-step solution

Let the object distance be u = -x and the image distance be v = 90 - x . Using the lens formula: 1 v - 1 u = 1 f Substituting the values: 1 90-x - 1 -x = 1 20 1 90-x + 1 x = 1 20 x + 90 - x x(90-x) = 1 20 90 90x - x^2 = 1 20 x^2 - 90x + 1800 = 0 Solving the quadratic equation: (x - 30)(x - 60) = 0 This gives x = 30 cm or x = 60 cm . For x = 30 cm , the image distance is v = 60 cm , and the magnification magnitude is |m| = 60 30 = 2 (magnified). For x = 60 cm , the image distance is v = 30 cm , and the magnification