Question

The image of the moon is focused by a converging lens of focal length $50\text{cm}$ on a plane screen. The image is seen by an unaided eye from a distance of $2.5\text{cm}$. Find the angular magnification achieved due to the converging lens.

• A. $2$
• B. $0.5$
• C. $3$
• D. $0.3$

Answer 1

The correct option is A $2$


Suppose the moon subtends on angle $\theta$ on the lens. This will also be equal to the angle subtended by the moon on the unaided eye.

The image of the moon is formed on the focal plane of the lens.

Size of the image, $h=f\theta$ [small angle approximation]

$h=50\theta$

This image is seen from a distance of $25\text{cm}$.

Angle formed by image on eye,

$\beta =\frac{h}{D}=\frac{50\theta }{25}=2\theta$

Now, Angular magnification,

$m=\frac{\beta }{\theta }=\frac{2\theta }{\theta }=2$

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

Key Concept: Angle subtended by an object (that is far away) on the lens is equal to angle subtended by the object on the unaided eye.