Question

Question #38eda

Answer 1

The above figure explains the phenomenon here. As per problem the lens mirror combination is so situateed with the object that the final image coincides with the object. This means that the retracing of rays has occurred here. It is only possible if the rays after refraction through the lens forms image at the center of curvature of the mirror.

Now proceeding towards calculation.

We know the lens formula as

`1/v-1/u=1/f`

where

`u->"object distance"=40cm`

`v->"image distance"=?`

`f->"focal length distance"=-15cm`

Inserting these in the equation

`1/v-1/40=-1/15`

`=>1/v=1/40-1/15=(3-8)/120=-1/24`

`v=-24cm`

So lens forms a real image at a distance 24cm from it and the center of curvature of the mirror should be at this position so that the emergent rays from lens when fall on the mirror retrace the path and final image is formed at the position of the object.

The focal length of the mirror given is 10cm. So its radius of curvature is `=2xx10=20cm`

Hence the distance between lens and mirror should be `24-20=4cm`