Ray Optics

JEE Main level, numerical answer, medium

163 of 295

Question 163 of 295

The distance between object and its two times magnified real image as produced by a convex lens is 45cm45cm. The focal length of the lens used is ________cmcm.

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Answer: 10

Magnification, m=vu=−2m=\dfrac{v}{u}=-2
⇒v=−2u…(i)\Rightarrow v=-2u\ldots \left(i\right)
As,
v−u=45…(ii)v-u=45\ldots \left(ii\right)
⇒u=−15cm\Rightarrow u=-15cm
Then, v=30cmv=30cm
From lens equation, we can write
1f=1v−1u⇒1f=130−1(−15)\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \Rightarrow \dfrac{1}{f}=\dfrac{1}{30}-\dfrac{1}{\left(-15\right)}
⇒f=+10cm\Rightarrow f=+10cm

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