question_answer

Light rays from a very distant source travel along the \[+x\] direction. Two identical thin lenses with focal length \[f>0\] and their optical axis along x, sit, one at \[x=0\] and the other at \[x=d<f\]. The rays focus at \[x=\]

A) \[d+\frac{f(f-d)}{2f-d}\]

B) \[d-\frac{f(f-d)}{d}\]

C) \[d+\frac{f(f-d)}{2(f+d)}\]

D) \[d+\frac{{{f}^{2}}}{2(f-d)}\]

Correct Answer: A

Solution :

[a] \[\frac{1}{v}-\left[ \frac{1}{(f-d)} \right]=\frac{1}{f}\] \[\Rightarrow \]   \[v=\frac{f(f-a)}{2f-d}\Rightarrow {{x}_{f}}=d+v=d+\frac{f(f-d)}{2f-d}\]