An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

Explanation

`{:("Concave mirror","Object","Image"),(r=+30 cm=2f,u=-20cm,v=? h.=?),(f=+15 cm,h=+5cm,"Nature of image = ?"):}`
Mirror formula `(l)/(v)+(l)/(u)=(l)/(f)`
`(l)/(v)+(1)/((-20))=(1)/((15)), (l)/(v)=(1)/(15)+(1)/(20), (l)/(v)=(7)/(60)`,
`v=+8.6 cm`
`m=-(v)/(u) rArr m=-(8.6)/((-20))=+0.43`
Magnification (m) `lt` l, indicates that the image is diminished.
`m=(h.)/(h)`
`0.43=(h.)/(h)`,
`h.=2.15 cm`.
The image is formed at a distance of 8.6 cm to the right of the convex mirror. The + sign signifies this. The height of the image is 2.15 cm. Image formed is erect, virtual and diminished.