Question 169 of 295

A point object $O$ is placed in front of two thin symmetrical coaxial convex lenses ${L}_{1}$ and ${L}_{2}$ with focal length $24cm$ and $9cm$ respectively. The distance between two lenses is $10cm$ and the object is placed $6cm$ 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: 34

For ${L}_{1}$:
$\dfrac{1}{{v}_{1}}+\dfrac{1}{6}=\dfrac{1}{24}$
$\Rightarrow \dfrac{1}{{v}_{1}}=\dfrac{1}{24}-\dfrac{1}{6}$
$=\dfrac{1-4}{24}$
$\Rightarrow \dfrac{1}{{v}_{1}}=\left(\dfrac{-3}{24}\right)$
$\Rightarrow {v}_{1}=–8cm$
For ${L}_{2}$:
$u=–18cm$
$\Rightarrow \dfrac{1}{v}+\dfrac{1}{18}=\dfrac{1}{9}$
$\Rightarrow \dfrac{1}{v}=\dfrac{1}{9}-\dfrac{1}{18}$
$=\dfrac{2-1}{18}$
$\Rightarrow \dfrac{1}{v}=\dfrac{1}{18}$
$\Rightarrow v=18cm$

Distance between object and distance $=16+18=34cm$.