Question

A convex lens of focal length $15\, cm$ is placed coaxially in front of a convex mirror. The lens is $5\, cm$ from the pole of the mirror. When an object is placed on the axis at a distance of $20\, cm$ from the lens, it is found that the image coineides with the object. Calculate the radius of curvature of the mirror - (consider all optical event) (in $cm$)

Answer 1

$f =15\, cm$

In absuce of convex mirror $I_{1}$ is the image formed by convex lens.
Since mirror is at distance $5\, cm$ from lens $So I_{1}$ is at distance $60-5=55\, cm$. From convex mirror.
Now final image $I_{2}$ is formed at $O$ it self, means rays after reflection from mirror incident on mirror normally.
Therefore $I_{1}$ is centre of curvature.
Hence $R_{1}=55 \,cm$.