Question

A real image is formed by a convex lens. If we put a concave lens in contact with it, the combination again forms a real image. The new image

• A. is closer to the lens system
• B. is farther from the lens system
• C. is at the original position
• D. may be anywhere depending on the focal length of the concave lens.

Answer 1

Answer: (B)

When concave lens is put in contact with convex lens, real/image is formed i.e., equivalent lens is convex. The focal length of equivalent lens F is greater than focal length of convex lens.
$\frac{1}{v}-\frac{1}{-u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{u-f}{fu}$
$v=\frac{uf}{u-f}=\frac{u}{\frac{u}{f}-1}$
As f increases, $\frac{u}{f}$ decreases
$\left(\frac{u}{f}-1\right)$ also decreases
Thus, v increases.