question_answer

A convex lens of focal length 15 cm is placed in , front of a convex mirror coaxially at a distance of 5cm from the pole of the mirror. When an object is placed at a distance of 20 cm from the lens, it is found that the image coincided with the object. Find the radius of curvature of the mirror.

Answer:

As the image coincides the object, the light rays retrace their path after reflection on the convex mirror. This shows the rays from lens incident normally on the mirror. So the image is formed at C by the lines. For lens, applying the lens formula, we get \[v=60\text{ }cm.\] Therefore the image is formed at distance of \[605=55\text{ }cm\] from the pole of the mirror. Therefore, the radius of curvature\[=55\text{ }cm.\]