Question

find the focal length of a convex lens which produces a real image to 60 cm from the lense when an aoject is placed at 40 cm in front of the lense

answer the question ​

Answer 1

Given,

for lens 1,

v = 60 cm

Let object distance be u.

$\large\rm { \frac {1}{f_{1}} = \frac {1}{v} - \frac {1}{u}}$

$\large\rm { \frac {1}{f_{1}} = \frac {1}{60} - \frac {1}{u}}$

$\large\rm { \frac {1}{f_{1}} = \frac {u+60}{60u}.....(1)}$

when the lenses are combined, the image distance $\large\rm { = v_{2} = 60-40 = 20cm }$

Let focal length of combination be F.

$\large\rm { \implies \frac {1}{F} = \frac {1}{f_{1}} + \frac {1}{f_{2}} = \frac {1}{20} + \frac {1}{u}}$

$\large\rm { \implies \frac {u+60}{60u} + \frac {1}{f_{2}} = \frac {1}{20} + \frac {1}{u}}$

$\large\rm { \frac {1}{f_{2}} = \frac {60u² + 1200u - 20u² - 1200u}{1200u²}}$

so, $\large\boxed{\rm { f_{2} = 30}}$