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  4. A convex mirror of focal length f forms an image which is (1/n) times the object. The distance of the object from the mirror is

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Q. A convex mirror of focal length $ f $ forms an image which is $ \frac{1}{n} $ times the object. The distance of the object from the mirror is

Jharkhand CECEJharkhand CECE 2012

Solution:

Given magnification,
$ m=\frac{1}{n} $
So, $ \frac{1}{n}=-\frac{v}{u} $
or $ v=-\frac{u}{n} $
By using mirror formula,
$ \frac{1}{f}=\frac{1}{v}+\frac{1}{u} $
$ =\frac{1}{-u/n}+\frac{1}{u} $
$ \Rightarrow $ $ u=-(n-1)f $