A convex lens of focal length 20 cm produces a virtual image of a real object. If the distance between the object and its virtual image is 45 cm , the linear magnification produced by the lens is ________.

Step-by-step solution

For a virtual image formed by a convex lens, both the object and the image lie on the same side of the lens, with the image being further away. Let the object distance be u = -x (where x > 0 ). The image distance is v = -(x + 45) . Using the lens formula: 1 v - 1 u = 1 f Substituting the values: 1 -(x + 45) - 1 -x = 1 20 1 x - 1 x + 45 = 1 20 x + 45 - x x(x + 45) = 1 20 45 x^2 + 45x = 1 20 x^2 + 45x - 900 = 0 Solving the quadratic equation: (x + 60)(x - 15) = 0 Since x must be positive, x = 15 cm . Thus, u = -15 cm