In the following diagram, an object ‘O’ is placed 15 cm in front o

1.	In the following diagram, an object ‘O’ is placed 15 cm in front of a convex lens L1 of focal length 20 cm and the final image is formed at ‘I’ at a distance of 80 cm from the second lens L2. Find the focal length of the lens L2.
Answer» For lens L₁ u = −15cm f = +20 cm using lens formula \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) \(\frac{1}{v}=\frac{1}{u}+\frac{1}{f}\) \(\frac{1}{v}=-\frac{1}{15}+\frac{1}{20}=-\frac{1}{60}\) v = −60 cm This image will act as object for lens L₂ lens u = −20 − 60 = −80cm v = + 80 cm \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) \(\frac{1}{80}+\frac{1}{80}=\frac{1}{f}\) \(\frac{1}{f}=\frac{1}{40}orf=40cm\)

In the following diagram, an object ‘O’ is placed 15 cm in front of a convex lens L1 of focal length 20 cm and the final image is formed at ‘I’ at a distance of 80 cm from the second lens L2. Find the focal length of the lens L2.

Answer»

For lens L₁

u = −15cm

f = +20 cm

using lens formula

\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

\(\frac{1}{v}=\frac{1}{u}+\frac{1}{f}\)

\(\frac{1}{v}=-\frac{1}{15}+\frac{1}{20}=-\frac{1}{60}\)

v = −60 cm

This image will act as object for lens L₂ lens

u = −20 − 60 = −80cm

v = + 80 cm

\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

\(\frac{1}{80}+\frac{1}{80}=\frac{1}{f}\)

\(\frac{1}{f}=\frac{1}{40}orf=40cm\)