Question 147 of 295

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :

A$30\mathrm{~cm}$B$3.75\mathrm{~cm}$C$15\mathrm{~cm}$D$7.5\mathrm{~cm}$

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Answer: (C) $15\mathrm{~cm}$

$\begin{aligned} & m=-3=-\frac{u}{v} \\ & u=-x \\ & v=-3 x \\ & \Rightarrow 2 x=20 \mathrm{~cm}\end{aligned}$
$\begin{aligned} & x=10 \mathrm{~cm} \\ & f=\frac{u V}{u+V}=\frac{(-10)(-30)}{(-10)+(-30)}=-7.5 \mathrm{~cm} \\ & f=-\frac{R}{2} \\ & R=-2 f=15 \mathrm{~cm}\end{aligned}$