A concave mirror possesses a focal length of 20 cm . Determine the...

Given the focal length of the concave mirror, $f = -20 \text{ cm}$.

The magnification produced by a mirror is given by $m = \dfrac{f}{f - u}$.

Since the image size is double the object size, the magnification can be either $m = -2$ (real image) or $m = +2$ (virtual image).

Case 1: For a real image, $m = -2$

$-2 = \dfrac{-20}{-20 - u}$

$40 + 2u = -20$

$2u = -60 \Rightarrow u = -30 \text{ cm}$

Case 2: For a virtual image, $m = +2$

$2 = \dfrac{-20}{-20 - u}$

$-40 - 2u = -20$

$-2u = 20 \Rightarrow u = -10 \text{ cm}$

The object can be placed at $10 \text{ cm}$ or $30 \text{ cm}$ from the mirror.