question_answer

A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. If a parellel beam of ligh falling on A leaves B as a parallel beam, then the distance d in cm will be

A)  25                         

B)         15  

C)  30                         

D)         50

Correct Answer: B

Solution :

 From the figure,              \[d={{f}_{1}}-{{f}_{2}}\] Mathematically,               \[\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}-\frac{d}{{{f}_{1}}{{f}_{2}}}=\frac{1}{F}\] For the emergent beam to be parallel,\[P=0,\,\,F=\propto \] \[\therefore \]  \[\frac{1}{20}-\frac{1}{5}+\frac{d}{100}=0\] \[\Rightarrow \]                                    \[d=15\]