Question

A convex lens (of focal length $20\text{cm}$) and a concave mirror, having their principal axes along the same lines, are kept $80\text{cm}$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30\text{cm}$ to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, would produce a virtual image by itself, would be:

• A. $25\text{cm}$
• B. $30\text{cm}$
• C. $10\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is C $10\text{cm}$


For lens,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{-30}=\frac{1}{20}$

$\therefore v=+60\text{cm}$

According to the condition, the image formed by the lens should be the centre of curvature of the mirror, and so,

$2f^{\prime }=20$ or $f^{\prime }=10\text{cm}$

The concave mirror forms a virtual image when the object is placed between focus and pole. So, the maximum distance of the object from the mirror, to obtain its virtual image, is $10\text{cm}$.

Hence, $\left(C\right)$ is the correct answer.