A point object is moving towards a convex mirror of focal length 20 cm with a speed of 25 cm/s. At a certain instant, the distance between the object and its image is 42 cm. The instantaneous speed of the image at this moment is

Step-by-step solution

For a convex mirror, the object is real ( u 0 ). The distance between the object and the image is given by D = |u| + v = -u + v . Given D = 42 cm, we have v - u = 42 v = 42 + u . Using the mirror formula: 1 v + 1 u = 1 f 1 42 + u + 1 u = 1 20 u + 42 + u u(42 + u) = 1 20 20(2u + 42) = u^2 + 42u 40u + 840 = u^2 + 42u u^2 + 2u - 840 = 0 Solving this quadratic equation: (u + 30)(u - 28) = 0 Since the object is real, u must be negative, so u = -30 cm. The image distance is v = 42 + (-30) = 12 cm. The transverse magnific