Question

A 2 cm long pin is placed perpendicular to the principal axis of a lens of focal length 15 cm at distance of 25 cm from the lens. Find the size of the image.

• A. The image of the pin is 3 cm long.
• B. The image of the pin is 2 cm long.
• C. The image of the pin is 5 cm long.
• D. The image of the pin is 10 cm long.

Answer 1

The correct option is A

The image of the pin is 3 cm long.

Here, u = - 25 cm, f = +15

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

$\frac{1}{v}$ - $\frac{1}{-25}$ = $\frac{1}{+15}$

v = 37.5 cm

The positive sign shows that the image is formed on the right -hand side of the lens.

Magnification is given by

m = $\frac{h^{/}}{h}$ = $\frac{v}{u}$

$\frac{h^{/}}{h}$ = $\frac{37.5}{-25}$ = - 1.5

h = - 1.5 $\times$ h = - 1.5 $\times$ 2 cm = - 3 cm

The image of the pin is 3 cm long. The negative sign shows that it is formed below the principal axis,i.e the image is inverted.