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Question

A man has a shaving mirror of focal length $$0.2\ m$$. How far should be held from his face in order to give an image of two fold magnification ?


Solution

Focal length of the Mirror $$f=-0.2\,m$$

Magnification $$m=2$$

We know that,

  $$ m=\dfrac{-v}{u} $$

 $$ v=-2u $$

Now, using the Mirror's Formula, (Concave Mirror)

  $$ \dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u} $$

 $$ \dfrac{1}{-0.2}=\dfrac{1}{-2u}+\dfrac{1}{u} $$

 $$ \dfrac{1}{2u}=\dfrac{1}{-0.2} $$

 $$ u=-0.1\,m $$

Hence, the man is standing at the distance of $$0.1\ m$$ from the saving mirror.


Physics

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