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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