Find the distance

Question:

Find the distance of the image from object $\mathrm{O}$, formed by the combination of lenses in the figure :

  1. $75 \mathrm{~cm}$

  2. $10 \mathrm{~cm}$

  3. $20 \mathrm{~cm}$

  4. infinity


Correct Option: 1

Solution:

$\frac{1}{V_{1}}+\frac{1}{30}=\frac{1}{10}$

$\frac{1}{V_{1}}=\frac{2}{30} \Rightarrow V_{1}=15 \mathrm{~cm}$

$\frac{1}{\mathrm{~V}_{2}}-\frac{1}{10}=-\frac{1}{10}$

$\frac{1}{\mathrm{~V}_{2}}=0 \quad \mathrm{~V}_{2}=\infty$

$\mathrm{V}_{3}=30 \mathrm{~cm}$

$\mathrm{OV}_{3}=75 \mathrm{~cm}$

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