An object is placed at a distance of `10 cm` from a convex mirror of focal length `15 cm`. Find the position and nature of the image ?

Explanation

Focal length of convex mirror, f = +15 cm
Object distance, u = -10 cm
According to the mirror formula,
Magnification, `m = ("Image distance")/("Object distance")=v/u`
`1/f = 1/v + 1/u`
`1/v=(1)/(15)-(1)/((-10))=(1)/(15)+(1)/(10)`
`1/v=(2+3)/(30)=(5)/(30) implies v = 6 cm`
The positive value of v indicates that the image is formed behind the mirror.
Magnification, `m = ("Height of image")/("Height of Object")=(h.)/(h)`
`=((-6))/((-10))=0.6`
The positive value of magnification indicates that the image formed is virtual and erect.