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Q.
If in the following figure, height of object is $ H_{1}=+2.5\,cm, $ then height of image $H_2$ formed is
Haryana PMTHaryana PMT 2007
Solution:
Magnification is ratio of size of image to that of object.
Here, $u=-1.5 f, f=-f$
From concave mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ we have,
$\frac{1}{(-f)}=\frac{1}{v}+\frac{1}{(-1.5 f)}$
$\therefore \frac{1}{v}=-\frac{1}{3 f}$
or $v=-3 \,f$
Now, magnification in mirror is given by
$m=\frac{I}{O}=\frac{v}{-u}$
where $I$ is size of image, and $0$ is size of object.
Here, $O=+2.5 \,cm$
$\therefore \frac{I}{2.5}=\frac{-3 \, f}{-(1.5 \, f)} $
$\therefore I=-5 \, c m$
In case of a concave mirror, magnification may be positive or negative, but in case of convex mirror magnification is positive only.
