Question

A converging lens has formed an image at a distance of 60 cm from the lens and the height of the image is $\frac{1}{4}$ the height of the object. Calculate the focal length of the lens.

• A. 36 cm
• B. 45 cm
• C. 48 cm
• D. 72 cm
• E. 80 cm

Answer 1

The correct option is C. 48 cm.

It is given that magnification of the lens is $-\frac{1}{4}$

We know that, for a lens the magnification is given by,

$m=\frac{h_i}{h_o}=\frac{v}{u}$

$⟹-\frac{1}{4}=\frac{v}{u}$

$⟹u=-4v=-240cm$

Using lens equation,

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

$=\frac{1}{60}-\frac{1}{-240}$

$=\frac{1}{48}$

$⟹f=48cm$