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A concave mirror produces three times enlarged real image of an object placed $25 cm$ in front of it. The Radius of curvature of the mirror will be.

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+ 20 cm

- 30 m

+ 25 mm

- 18 cm

answer is D.

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Detailed Solution

The Radius of curvature of the mirror

R = - 18 cm

Given,
Distance of the object from the mirror,

u = - 12 cm

, and magnification,

m = - 3

m = - \frac{v}{u}, hence

v = - mu

= - (- 3) \times - 12

= - 36 cm

We know that

\Rightarrow \frac{1}{f} = \frac{1}{v} + \frac{1}{u}

\Rightarrow \frac{1}{- 36} + \frac{1}{- 12}

\Rightarrow \frac{- 1 - 3}{36}

\Rightarrow - \frac{4}{36}

\Rightarrow - \frac{1}{9}

\Rightarrow f = - 9 cm

The radius of curvature of given the mirror is

R = 2 f

= 2 \times - 9

= - 18 cm

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