A convex lens A of focal length $20 \mathrm{~cm}$ and a concave lens B of focal length $56 \mathrm{~cm}$ are…
A convex lens A of focal length $20 \mathrm{~cm}$ and a concave lens B of focal length $56 \mathrm{~cm}$ are kept along the same axis with the distance $d$ between them. If a parallel beam of light falling on A leaves B as a parallel beam, then the magnitude of distance $d$ (in $\mathrm{cm}$ ) is
25
36
30
50
Solution
$d=f_1+f_2$
By using the formula
$\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1 f_2}=\frac{1}{f}$
For the emergent beam to parallel
$\begin{aligned}
& P=0 \text { or } f=\propto \\
& \Rightarrow \frac{1}{20 \mathrm{~cm}}+\frac{1}{(-56 \mathrm{~cm})}-\frac{d}{20 \mathrm{~cm}(-56 \mathrm{~cm})}=0 \\
& \therefore d=20 \mathrm{~cm}+(-56 \mathrm{~cm})=-36 \mathrm{~cm}
\end{aligned}$