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  4. The correct relation between the linear magnification m, the object distance u and the focal length f, for a mirror is given by

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Q. The correct relation between the linear magnification m, the object distance u and the focal length $ f, $ for a mirror is given by

CMC MedicalCMC Medical 2012

Solution:

Magnification, $ m=\frac{-v}{u} $ But $ \frac{1}{f}=\frac{1}{v}-\frac{1}{u} $ (Mirror formula) $ \Rightarrow $ $ \frac{u}{f}=\frac{u}{v}+1 $ $ \Rightarrow $ $ -\frac{u}{v}=1-\frac{u}{f} $ $ \Rightarrow $ $ \frac{-v}{u}=\frac{f}{f-u} $ So, $ m=\frac{f}{f-u} $