Question

Image of an object at infinity is formed by a convex lens of focal length $30cm$ such that the size of the image is $2cm$. If a concave lens of focal length $20cm$ is placed in between the convex lens and the image, at a distance $26cm$ from the convex lens, size of the new image is:

Answer 1

Without the concave lens, image is formed at a distance 30 cm from the convex lens. When concave lens is placed, it serves as the object for the concave lens.

Hence, for concave lens, $u=4cm$

Given, $f=-20cm$

From lens formula,

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

$\frac{1}{v}=\frac{1}{4}+\frac{1}{-20}=\frac{4}{20}$

$v=5cm$

Magnification of lens, $m=\frac{v}{u}=\frac{5}{4}$

Magnification of lens, $m=\frac{h_I}{h_o}$

$⟹h_I=2\times 1.25=2.5cm$