Question

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length $30cm$ is $2cm$. If a concave lens of focal length $20cm$ is placed between the convex lens and the image at a distance of $26cm$ from the convex lens, calculate the new size of the image.

• A. $1.25cm$
• B. $2.5cm$
• C. $1.05cm$
• D. $2cm$

Answer 1

Answer: (B)

Convex lens forms the image at $I_1.I_1$ is at the second focus of convex lens. Size of
$I_1=2cm$.
$I_1$ acts as virtual object for concave lens. Concave lens forms the image of $I_1$ at $I_2$

Lens formula : $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
For concave lens,
$\frac{1}{v}-\frac{1}{4}=-\frac{1}{20}$
or $\frac{1}{v}=-\frac{1}{20}+\frac{1}{4}$
$=\frac{4}{20}=\frac{1}{5}$
or $v=5cm=$ Distance of $I_2$ from concave lens.
$\therefore$ Magnification $=\frac{v}{u}$
$=\frac{\text{size of image}}{\text{size of object}}=\frac{5}{4}$
$\therefore \frac{\text{size of image}}{2}=1.25$
$\therefore$ size of image due to concave lens $=2.5cm$