A point object $O$ is placed in front of two thin symmetrical coaxial convex lenses $L_{1}$ and $L_{2}$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed is placed 6 cm away from lens $L_{1}$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is ……… cm.

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answer is 34.

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Detailed Solution

Question Image
For $L_{1}$
$\frac{1}{υ_{1}} + \frac{1}{6} = \frac{1}{24} \Rightarrow \frac{1}{υ_{1}} = \frac{1}{24} - \frac{1}{6} = \frac{1 - 4}{24}$
$\Rightarrow \frac{1}{υ_{1}} = (\frac{- 3}{24}) \Rightarrow υ_{1} = - 8 c m$
For $L_{2}$
$u = - 18 c m$
$\Rightarrow \frac{1}{υ} + \frac{1}{18} = \frac{1}{9}$
$\Rightarrow \frac{1}{υ} = \frac{1}{9} - \frac{1}{18}$
$\Rightarrow \frac{2 - 1}{18}$
$\Rightarrow \frac{1}{υ} = \frac{1}{18} \Rightarrow υ = 18 c m$
Question Image
Distance between object and distance $= 16 + 18 = 34 c m$

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