If the distance between object and its two times magnified virtual...

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm , the focal length of the mirror must be:

Options

A $\frac{10}{3} \mathrm{ cm}$
B $-12 \mathrm{ cm}$
C $-10 \mathrm{ cm}$
D15 cm

Correct answer

C. $-10 \mathrm{ cm}$

Step-by-step solution

Since, image is magnified. So, it is a concave mirror.

\therefore \mathrm{m}=2=\frac{-\mathrm{v}}{\mathrm{u}}2=\frac{-(15-u)}{-u}2 u=15-u3 \mathrm{u}=15 \Rightarrow \mathrm{u}=5 \mathrm{ cm}\mathrm{v}=15-\mathrm{u}=15-5=10 \mathrm{ cm}

Bymirror formula,

\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{10}+\frac{1}{(-5)}=\frac{1-2}{10}=\frac{-1}{10}\mathrm{f}=-10 \mathrm{ cm}

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