Write the formula for a lens connecting image distance (v), object distance (u) and the focal length (f). How does the lens formula differ from the mirror formula?

The formula for a lens connecting image distance $(v)$, object distance $(u)$, and the focal length $(f)$ is:

$\frac {1}{v}-\frac {1}{u}=\frac {1}{f}$     (Lens formula)

Now, the mirror formula is given by:

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

In both the formulas,

$u$ = Object distance

$v$ = Image distance

$f$ = Focal length

In the mirror formula, a positive sign $(+)$ is present between the reciprocals of image distance $(\frac {1}{v})$ and object distance $(\frac {1}{u})$.

Whereas, in the lens formula, a negative sign $(-)$ is present between the reciprocals of image distance $(\frac {1}{v})$ and object distance $(\frac {1}{u})$.

So the lens formula differs from the mirror formula by the negative sign $(-)$ which is present between the reciprocals of image distance, and object distance.