The image of an extended object, positioned perpendicular to the...

The lateral magnification for a spherical or plane mirror is given by $m = -\dfrac{v}{u}$.

For an erect image, the magnification $m$ must be positive, which means $m > 0$.

$\Rightarrow -\dfrac{v}{u} > 0 \Rightarrow \dfrac{v}{u} < 0$

This implies that the object distance $u$ and the image distance $v$ must have opposite signs.

According to the Cartesian sign convention, a real object has $u < 0$ and a virtual object has $u > 0$. Similarly, a real image has $v < 0$ and a virtual image has $v > 0$.

Since $u$ and $v$ must have opposite signs, there are two valid conditions.

First condition: $u < 0$ (real object)$and v > 0$ (virtual image).

Second condition: $u > 0$ (virtual object)$and v < 0$ (real image).

Thus, an erect image is formed when the object is real while the image is virtual, or when the object is virtual while the image is real.