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  4. An object is kept at a distance of 60 cm from a concave mirror. For getting a magnification of (1/2), focal length of the concave mirror required is

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Q. An object is kept at a distance of $60\,cm$ from a concave mirror. For getting a magnification of $\frac{1}{2}$, focal length of the concave mirror required is

KEAMKEAM 2012Ray Optics and Optical Instruments

Solution:

$ m=-\frac{v}{u} $
$ \frac{1}{2} =-\frac{v}{60} $
$ v =-30\,cm $
$ \frac{1}{f} =\frac{1}{v}-\frac{1}{u} $
$ \frac{1}{f} =\frac{1}{-30}+\frac{1}{-60} $
$ \frac{1}{f} =-\frac{-2-1}{60}=\frac{-3}{60} $
$ f=-20 \,cm$