Question

A concave lens forms the image of an object such that the distance between the object and image is $10cm$ and the magnification produced is $1/4$. The focal length of the lens will be

• A. $8.6cm$
• B. $6.2cm$
• C. $10cm$
• D. $4.4cm$

Answer 1

The correct option is D $4.4cm$

The correct option is D.

Given,

The distance between the object and mirror $=10cm$ and magnification is $\frac{1}{4}$

Magnification is the ratio of the height of the image with the height of the object

$=\frac{v}{u}$

$u-v=10cm$

$v=u-10cm$

$\Rightarrow \frac{v}{u}=\frac{u-10}{u}=\frac{1}{4}$

$\Rightarrow 4u-40=u$

$u=\frac{40}{3}cm$

$v=\frac{10}{3}cm$

Now,

By Lens formula:

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

$\frac{1}{f}=\frac{3}{10}-\frac{3}{40}$

$\frac{1}{f}=\frac{9}{40}$

$f=\frac{40}{9}cm$

Focal length, $f=4.4cm$