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

Explanation

Object distance, `u=-27 cm`
Object hight, 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)`
The screem should be placed at distance of 54 cm in front of the given mirror.
Magnification,
`m=("Image Distance")/("Object Distance")=(-54)/(27)=-2`
The negative value of magnification indicate that the image formed is real.
Magnification, `m=("Height of the Image")/("Height of the Object")=(h^(1))/(h)`
`h^(1)=7xx(-2)=-14 cm`
The negative value of image height indicates that the image formed is inverted.