MHT CET · Physics · Ray Optics
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
- A 25
- B 36
- C 30
- D 50
Answer & Solution
Correct Answer
(B) 36
Step-by-step Solution
Detailed explanation
\(d=f_1+f_2\)
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
\(\begin{aligned}
& P=0 \text { or } f=\propto \\
& \Rightarrow \frac{1}{20 \mathrm{~cm}}+\frac{1}{(-56 \mathrm{~cm})}-\frac{d}{20 \mathrm{~cm}(-56 \mathrm{~cm})}=0 \\
& \therefore d=20 \mathrm{~cm}+(-56 \mathrm{~cm})=-36 \mathrm{~cm}
\end{aligned}\)
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
\(\begin{aligned}
& P=0 \text { or } f=\propto \\
& \Rightarrow \frac{1}{20 \mathrm{~cm}}+\frac{1}{(-56 \mathrm{~cm})}-\frac{d}{20 \mathrm{~cm}(-56 \mathrm{~cm})}=0 \\
& \therefore d=20 \mathrm{~cm}+(-56 \mathrm{~cm})=-36 \mathrm{~cm}
\end{aligned}\)
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