question_answer

A luminous object is placed at a distance of 30 cm from a convex lens of focal length 20 cm. At what distance from the lens, on the other side, must a convex mirror of radius of curvature 10 cm be placed, in order to have an upright image of the object coincident with it?

A)  12 cm                        

B)  30 cm

C)  50 cm                        

D)  60 cm

Correct Answer: C

Solution :

This is possible when the rays are incident on the mirror normally, i,e., the image by the lens is formed at the center of curvature of the mirror. Now, \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]or \[\frac{1}{20}=\frac{1}{v}+\frac{1}{-30}\] or\[v=60\]From the figure, the distance of mirror from lens, \[LM=LC-MC=60-10=50\text{ }cm.\]Hence, the correction option is [c].