Find the position of an object that, when placed in front of a concave mirror of a focal length of 20 cm, produces a virtual image that is twice the size of the object.

The position of an object that, when placed in front of a concave mirror, is

10 cm

.
Given ,

f = - 20 cm, (Negative : as the mirror is concave) m = + 2

(positive due to the image is virtual & erect)

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

v = - 2 u

Now by using mirror formula,

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

\Rightarrow \frac{1}{- 20} = \frac{1}{u} - \frac{1}{2 u}

\Rightarrow \frac{1}{- 20} = \frac{1}{2 u}

u = - 10 cm

So the object is placed at a distance of

10 cm

from the mirror.

Find the position of an object that, when placed in front of a concave mirror of a focal length of $20 cm$ , produces a virtual image that is twice the size of the object.