Question 29 of 295

If the distance between object and its two times magnified virtual image produced by a curved mirror is $15cm$, the focal length of the mirror must be :

A$15cm$B$-12cm$C$-10cm$D$\dfrac{10}{3}cm$

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Answer: (C) $-10cm$

Let object be at a distance $xcm$ from the pole. Then, distance of image from the pole will be $=15-x$.
Given:
Magnification, $m=2=\dfrac{-v}{u}$
$\Rightarrow 2=\dfrac{-(15-x)}{-x}$
$\Rightarrow 2x=15-x$
$\Rightarrow 3x=15 \Rightarrow x=5cm$
Now,
Distance of the image from the pole $=15-x=15-5=10cm$
Therefore, $v=10cm$
From mirror formula:
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$
$=\dfrac{1}{10}+\dfrac{1}{(-5)}=\dfrac{1-2}{10}=\dfrac{-1}{10}$
$\Rightarrow f=-10cm$

JEE Main Physics practice question on Ray Optics (Mirror Formula, Reflection in Spherical Mirror), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.