Three lenses L₁, L₂, L₃ are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens L₁, emerging L₃ as a convergent beam such that it converges at the focus of L₃. Distance between L₁ and L₂ will be

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40 cm

30 cm

20 cm

10 cm

answer is C.

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Detailed Solution

According to the problem, combination of L₁ and L₂ act a simple glass plate. Hence according to formula $\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}$
$\begin{array}{l} \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}} = 0 \Rightarrow \frac{1}{f_{1}} + \frac{1}{f_{2}} = \frac{d}{f_{1} f_{2}} \\ \Rightarrow \frac{1}{30} - \frac{1}{10} = \frac{d}{30 \times - 10} \Rightarrow \frac{- 20}{30 \times 10} = - \frac{d}{30 \times 10} \\ \Rightarrow d = 20 cm \end{array}$