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# A person looks in to a spherical mirror . The size of image of his face is twice the actual size of his face. If the face is at distance 20 cm then find the radius of curvature of mirror.

$(a)\;20 \;cm \\ (b)\;40 \;cm \\ (c)\;60\;cm \\ (d)\;80\;cm$

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A)
Person will see his face only when image of real object is erect.
So $m=2$ and $u=-20$
$\therefore \large\frac{-v}{u}$$=2$
$v= 40\;cm$
Applying $\large\frac{1}{v}+\frac{1}{u} =\frac{1}{f}$
$f= -40 \;cm$ or $R= 80\;cm$
Hence d is the correct answer.

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A)
yes