An object of size `7.0 cm` is placed at `27 cm` in front of a concave mirror of focal length `18 cm`. At what distance from the mirror, should a screen be placed, so that a sharp focussed image can be obtained ? Find the size and nature of the image ?

Explanation

Object distance, u = −27 cm
Object height, h = 7 cm
Focal length, f = −18 cm
According to the mirror formula,
`1/v-1/u=1/f`
`1/v=1/f-1/u`
`=(-1)/18+1/27=(-1)/54`
v = -54 cm
The screen should be placed at a distance of 54 cm in front of the given mirror.
`"Magnification," m= -("Image Distance")/("Object Distance")=(-54)/27= -2`
The negative value of magnification indicates that the image formed is real.
`"Magnification," m=("Height of the Image")/("Height of the Object")=(h')/h`
`h'=7xx(-2)=-14 cm`
The negative value of image height indicates that the image formed is inverted.