Question

A convex lens forms image at a distance 60 cm from the lens for an object placed on its principal axis. If one more convex lens is placed in contact with first one then image shifts closer to combination by 40 cm. Focal length of second lens in cm is:

• A. 20
• B. 30
• C. 40
• D. 50

Answer 1

The correct option is B 30

Given,

for lens 1,

Image distance, $v=60cm$

let object distance be $u$

$\frac{1}{f_1}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f_1}=\frac{1}{60}+\frac{1}{u}$

$\frac{1}{f_1}=\frac{u+60}{60u}....\left(1\right)$

when the lenses are combined, the image distance $=v_2=60-40=20cm$

Focal length of the combination be $F$

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{v_2}-\frac{1}{u}$

$\Rightarrow$ $\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{20}+\frac{1}{u}$

$\Rightarrow$ $\frac{u+60}{60u}+\frac{1}{f_2}=\frac{1}{20}+\frac{1}{u}$

$\Rightarrow$ $\frac{1}{f_2}=\frac{u+20}{20u}-\frac{u+60}{60u}$

$\frac{1}{f_2}=\frac{60u^2+1200u-20u^2-1200u}{1200u^2}$

$=\frac{40u^2}{1200u^2}$

$f_2=30cm$