Question

A lens forms a real image of an object on a screen placed at a distance of 100 cm from the screen. If the lens is moved by 20 cm towards the screen, another image of the object is formed on the screen. The focal length of the lens is:

• A. 12 cm
• B. 24 cm
• C. 36 cm
• D. 48 cm

Answer 1

The correct option is B 24 cm

From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{100-u}+\frac{1}{u}=\frac{1}{f}$.....(1)

$\frac{1}{80-u}+\frac{1}{u+20}=\frac{1}{f}$........(2)

From (1) and (2),

$\frac{1}{100-u}+\frac{1}{u}=\frac{1}{80-u}+\frac{1}{u+20}$

$\frac{20}{\left(u\right)(u+20)}=\frac{20}{(80-u)(100-u)}$

$\Rightarrow u^2+20u=u^2-180u+8000$

$\Rightarrow u=40$

$\frac{1}{60}+\frac{1}{40}=\frac{1}{f}$

$\Rightarrow f=24cm$