To get an image of magnification $-1$ on a screen using a lens of focal length $20\text{ cm}$, the object distance must be :

The magnification of a lens is given by the formula $m = \frac{v}{u}$, where $v$ is the image distance and $u$ is the object distance. For a magnification of $-1$, the image distance is equal to the object distance. Using the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$, where $f$ is the focal length, we can find the object distance. Substituting $v = u$ and $f = 20\text{ cm}$, we get $\frac{1}{u} - \frac{1}{u} = \frac{1}{20}$, which simplifies to $\frac{1}{u} = \frac{1}{40}$. Therefore, the object distance must be $40\text{ cm}$.