What is Mirror Formula?

In short

The mirror formula connects the object distance $u$ , the image distance $v$ and the focal length $f$ of a spherical mirror: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ .

In simple words

Use the New Cartesian sign convention: distances are measured from the pole of the mirror, the direction of the incident light is positive, and distances against it are negative. An object in front of a concave mirror has a negative $u$ and a negative $f$ . A negative $v$ means a real image in front of the mirror, and a positive $v$ means a virtual image behind it.

Example

An object stands $30\ \text{cm}$ in front of a concave mirror of focal length $20\ \text{cm}$ . With $u = -30\ \text{cm}$ and $f = -20\ \text{cm}$ , $\dfrac{1}{v} = \dfrac{1}{-20} + \dfrac{1}{30} = -\dfrac{1}{60}$ , so $v = -60\ \text{cm}$ . The image is real, $60\ \text{cm}$ in front of the mirror.