Using mirror formula, explain why does a convex mirror always produce a virtual image.

Explanation

Deduction of mirror formula
`(1)/(v) + (1)/(u) = (1)/(f)`
For a convex mirror f is always +ve.
`therefore f gt c`
Object is always placed in front of mirror hence `u lt 0` (for real object)
`(1)/(v) + (1)/(u) = (1)/(f)`
`rArr (1)/(v) = (1)/(f) -(1)/(u)`
`"As " u lt 0 u -ve " hence"`
`(1)/(v) gt 0`
`rArr v gt i.e.+ve " for all values of u. "`
image will be formed behind the mirror and it will be virtual for all values of u.