When an object is placed at a distance of 25 cm from a mirror, the magnification is `m_(1)`. The object is moved 15cm farther away with respect to the earlier position, and the magnification becomes `m_(2)`. If `m_(1)//m_(2)=4` , then calculate the focal length of the mirror.

Explanation

We know that `m=-(v)/(u)=(f)/(f-u)`
Here, `m_(1)=(f)/(f-(-25))=(f)/(f+25)` and
`m_(2)=(f)/(f-(-25-15))=(f)/(f+40)`
Since ` (m_(1))/(m_(2))=4, ` therefore `(f+40)/(f+25)=4`
`f+40=4f+100`
or `f=-20 cm`
The negative sign shows that the mirror is concave.