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Byju's Answer

Standard XII

Physics

Lens Maker's Formula

Three lenses ...

Question

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 $L_{1}$ , emerging $L_{3}$ as a convergent beam such that it converges at the focus of $L_{3}$ . Distance between $L_{1}$ and $L_{2}$ will be

40 cm

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30 cm

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20 cm

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10 cm

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Solution

The correct option is C 20 cm
According to the problem, combination of $L_{1}$ and $L_{2}$ act a simple glass plate. Hence according to formula
$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}$
$\frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}} = 0 \Rightarrow \frac{1}{f_{1}} + \frac{1}{f_{2}} = \frac{d}{f_{1} f_{2}}$
$\Rightarrow \frac{1}{30} - \frac{1}{10} = \frac{d}{30 \times - 10} \Rightarrow \frac{- 20}{30 \times 10} = - \frac{d}{30 \times 10}$
$\Rightarrow d = 20 c m$

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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

The correct option is C 20 cmAccording to the problem, combination of L1 and L2 act a simple glass plate. Hence according to formula 1F=1f1+1f2−df1f2 1f1+1f2−df1f2=0⇒1f1+1f2=df1f2 ⇒130−110=d30×−10⇒−2030×10=−d30×10 ⇒d=20 cm