The object should be placed 5 cm in front of a concave mirror so that the image is magnified 2 times.
Explanation:
Using mirror formula:
[tex]\frac{1}{v}+\frac{1}{u} = \frac{1}{f}[/tex]
v = Distance of image from the mirror
u = Distance of object from the mirror
f = Focal length of the mirror
According to Cartesian sign convention, Virtual distances are taken as negative and the real distances are taken as positive. We are given that the focal length of the mirror is 10 cm and the image is magnified two times.
We know that the magnification is given by the formula:
[tex]M = -\frac{v}{u}\\2 = -v/u\\v = -2u[/tex]
Using this equation in the mirror formula, we get:
[tex]\frac{1}{-2u} +\frac{1}{u} =\frac{1}{f}[/tex]
[tex]\frac{1}{-2u}+\frac{1}{u}=\frac{1}{10}\\\frac{10}{-2u}+\frac{10}{u} = 1\\\frac{-5}{u} +\frac{10}{u} = 1\\Multiplying-by-'u'-on-both-sides:\\-5+10 = u\\=> u = 5[/tex]
Hence, the object should be placed 5 cm away from the mirror and the image formed is virtual and magnified two times.
Keywords: magnification, mirrors, image formation
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