Question

A pin 3 cm long is placed at a distance of 24 cm from a convex lens of focal length 18 cm. The pin is placed perpendicular to the principal axis. Find the size and nature of the image.

• A. 9 cm, erect
• B. 9 cm, inverted
• C. 12 cm, inverted
• D. 12 cm, erect

Answer 1

The correct option is B

9 cm, inverted

Here, u = - 24 cm, f = + 18 cm , v = ?

Using the len's formula, $\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$ we get

$\frac{1}{v}$ - $\frac{1}{-24}$ = $\frac{1}{+18}$

v = 72 cm

The image is formed 72 cm from the lens on the other side. So the image is real.

Magnification, $m=\frac{h^{\prime }}{h}$ = $\frac{v}{u}$ = $\frac{72}{-24}=-3$

$h^{\prime }=-3\times h=-3\times 3.0=-9cm$

The image is 9 cm in size. Negative sign shows that the image is inverted.