A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses and with focal length 24 cm and 9 cm respectively. [2023]

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Solution

Q.
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 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. [2023]

Ans.
(34)

$From 1^{st} lens \frac{1}{v} + \frac{1}{6} = \frac{1}{24}$

$\frac{1}{v} = \frac{1}{24} - \frac{1}{6} = - \frac{1}{8} \Rightarrow v = - 8 cm$

$From 2^{nd} lens \frac{1}{v} + \frac{1}{18} = \frac{1}{9}$

$\frac{1}{v} = \frac{1}{9} - \frac{1}{18} = \frac{1}{18} \Rightarrow v = 18$

So distance between object and its image $= 6 + 10 + 18 = 34 cm$

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