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  4. Radius of curvature of concave mirror is 40 cm and the size of image is twice as that of object, then the object distance is

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Q. Radius of curvature of concave mirror is $40 \,cm$ and the size of image is twice as that of object, then the object distance is

Chhattisgarh PMTChhattisgarh PMT 2007

Solution:

Given, $R=2 f=40\, cm$.
$\therefore f=20\, cm $
$m=2 m=\frac{v}{u}=2$
$\therefore v=2 \,u$
Using mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{20}=\frac{1}{2 u}+\frac{1}{u}=\frac{1+2}{2 u}$
$u=30 \,cm$