The spherical mirror formula is `(1)/(u) + (1)/(v) = (1)/(f)` …(i)
For a plane mirror, `R = oo`
`f = (R )/(2) = oo`
Form (i), `(1)/(u) + (1)/(v) = (1)/(oo) = 0` or `(1)/(v) = -(1)/(u)`
or `v = -u`
As `u` is negative, `v` becomes +.
Hence, image is formed behind the mirror at the same distance as the object is in front of it. This is what happens in a plane mirror. Hence the desired result.
