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A point object is placed on the principal axis of a convex lens of focal length 15 cm at a distance of 30 cm from it. A convex mirror of radius of curvature 20 cm is placed on the other side of the lens such that the principal axes of both the lens and the mirror coincide. If the final image formed by the combination coincides with the object itself, the distance between the convex lens and the convex mirror is ____

Correct answer

10

Step-by-step solution

For the final image to coincide with the object, the light rays must retrace their path after reflection from the convex mirror. This happens when the rays strike the mirror normally, meaning they are directed towards its centre of curvature. First, find the position of the image formed by the convex lens alone. Using the lens formula: 1 v - 1 u = 1 f Given u = -30 cm and f = +15 cm : 1 v - 1 -30 = 1 15 1 v = 1 15 - 1 30 = 1 30 v = +30 cm The image formed by the lens is at 30 cm from the lens. For the rays to be di

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