Solution

Conversely, we may ask where a light source should be placed in order that its image is formed $40$ cm behind the mirror. Using half the radius of curvature of the mirror as its focal length, we have

$$u=\frac{vf}{v-f}=\frac{-40\cdot40}{-40-40}=20.$$

Therefore, the object should be placed $20$ cm from the focal point toward the mirror.