A small candle `2.5 cm` in size is placed `27 cm` in front of a concave mirror of radius of curvature `36 cm`. At what distance from the mirror should a screen be placed in order to receive a sharp image ? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved ?

Explanation

Given, object distance, `u=-27cm`
Radius of curvature of mirror, `R=-36cm` (concave mirror)
`therefore" focal length, f"=(R )/(2)=(-36)/(2)=-18cm`
From mirror formula,
`(1)/(u)+(1)/(v)=(1)/(f)`
`rArr" "-(1)/(27)+(1)/(v)=-(1)/(18)`
`rArr" "(1)/(v)=(1)/(27)-(1)/(18)`
`rArr" "(1)/(v)=(2-3)/(54)=-(1)/(54)`
`rArr" "v=-54cm`
The screen should be placed 54 cm from the mirror, on the same side as the object.
`"Magnification, m"=(h_(i))/(h_(o))=-(v)/(u)`
`rArr" "(h_(1))/(2.5)=-(54)/(27)`
`therefore" "h_(1)=-5cm`
i.e. the image is real, inverted and magnified.
If the candle is moved closer to the mirror, the screen would have to be moved farther and farther from the mirror. When the distance of the candle from the mirror is made less than 18 cm (focal length), the image becomes virtual and cannot be obtained on the screen.