Question

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 1

As per the figure,
The image formed by lens L₁ is at I'. Therefore, using lens formula

\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]

As per the parameters given in the question

\[u = - 15 cm\]

\[ f_{L

_1} = 20 cm\]

So, the image distance will be

\[\frac{1}{v} - \frac{1}{( - 15)} = \frac{1}{20}\]

\[v = - 60 cm\]

Now, this image is acting as an object for the lens L₂ . We can again use the lens formula and other parameters given in the question and question figure to find the focal length of lens L₂.

\[\frac{1}{v_{L_2}} - \frac{1}{u_{L_2}} = \frac{1}{f_{L_2}}\]

Here, 

\[u_{L_2} = v + ( - 20) = - 80 cm\]

\[ v_{L_2} = 80 cm\]

\[\frac{1}{80} - \frac{1}{\left( - 80 \right)} = \frac{1}{f_{L_2}}\]

\[ f_{L_2} = 40 cm\]

So, the focal length of the lens L₂ = 40 cm.