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Question

# A point source S is placed at a distance of 15cm from a converging lens of focal length 10cm on its principal axis. Where should a diverging mirror of focal length 12cm be placed so that a real image is formed on the source itself?

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Solution

## Formula for refraction through the lens is, u=−15cm and f=±10cm1v+115=110v=30cmAs v is positive,the image I1,is formed to the right of lens.The convex mirror is to be placed to the right of lens in such a way hat light rays fall on the mirror normally.Then only the light rays will retrace their path and form final image on the object itself.This shows that image I1 formed by the lens should be at the center of curvature of the mirror i.e,PI1=R=2f=24cmAs |v|=OI1=30cm. ,Hence OP=30−24=6cmThus,the convex mirror should be placed at a distance of 6cm to the right of lens

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