A point object is placed at a distance of $u=-30\text{ cm}$ from a convex lens of focal length $f=20\text{ cm}$. A convex mirror of radius of curvature $R=20\text{ cm}$ is placed $50\text{ cm}$ behind the lens. Find the position of the final image formed by this system.

Solution

1. For the convex lens, use the lens formula $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ with $u=-30\text{ cm}$ and $f=20\text{ cm}$ to find $v=60\text{ cm}$.
2. The lens forms an image $60\text{ cm}$ behind it, which is $10\text{ cm}$ behind the convex mirror placed $50\text{ cm}$ from the lens.
3. Since the mirror has a radius of curvature $R=20\text{ cm}$, the image formed by the lens lies exactly at the mirror's center of curvature.
4. Light rays directed toward the center of curvature of a mirror reflect back along the same path, meaning the final image forms at the pole of the mirror.
5. Hence the answer is (A).