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 focused image can be obtained ? Find the size and the nature of the image.

Explanation

`{:("Concave mirror","Object","Image"),(f=-18 cm,u=-27 cm,v=? h.=?),(r=2f=-36 cm,h=+7 cm,"Nature of image = ?"):}`
Mirror formula : `(l)/(v)+(l)/(u)=(l)/(f)`
`(l)/(v)+(1)/((-27))=(1)/((-18)), (l)/(v)=-(1)/(18)+(1)/(27), (l)/(v)=-(1)/(54)`
`v=-54 cm`
`m=-(v)/(u), " " m=-((-54))/((-27))=-2`
Magnification `(m) gt 1`, indicates that the image is enlarged.
`m=(h.)/(h), " "-2=(h.)/(7), h.=-14 cm`
The image is formed at a distance of 54 cm to the left of the concave mirror. The - sign signifies this. The height of the image is 14 cm. The -ve sign indicates that the image formed is real, inverted. The image formed is real, inverted and enlarged.