Question

If the size of a virtual image formed by a concave mirror of focal length 15 cm is twice the size of the object, then distance of object from mirror is -

• A. $15cm$
• B. $10cm$
• C. $7.5cm$
• D. $5cm$

Answer 1

The correct option is C $7.5cm$

Given $f=15cm$

Since the image is twice the size of the object the magnification can be written as

$m=2=-\frac{v}{u}$

$\Rightarrow v=-2u$

Since the image is virtual, $v$ is positive.

The mirror formula is given as

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

$\Rightarrow \frac{1}{15}=\frac{1}{u}+\frac{1}{-2u}$

$\Rightarrow \frac{1}{15}=\frac{2-1}{2u}=\frac{1}{2u}$

$\therefore 2u=15$

$\Rightarrow u=7.5cm$

Hence the correct answer is option (C).