Show that the mirror formula for spherical mirrors also holds for a plane mirror.

(N/A) The mirror formula is given by $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.
For a plane mirror,the focal length $f$ is considered to be infinity $(\infty)$.
Substituting $f = \infty$ into the mirror formula,we get:
$\frac{1}{v} + \frac{1}{u} = \frac{1}{\infty}$
Since $\frac{1}{\infty} = 0$,the equation becomes:
$\frac{1}{v} + \frac{1}{u} = 0$
$\frac{1}{v} = -\frac{1}{u}$
$v = -u$
This result shows that for a plane mirror,the image distance $v$ is equal in magnitude to the object distance $u$ but opposite in sign,which is consistent with the properties of plane mirrors (virtual image formed at the same distance behind the mirror).