Question

A convex lens of focal length $15cm$ is placed coaxially in front of a convex mirror. The lens is $5cm$ from the pole of the mirror. When an object is placed on the axis at a distance of $20cm$ 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

Answer: 55.00

$f=15cm$

In absuce of convex mirror $I_1$ is the image formed by convex lens.
Since mirror is at distance $5cm$ from lens $So{I}_1$ is at distance $60-5=55cm$. 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 $R_1=55cm$.