A convex mirror used for rear view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and magnification of the image.

Explanation

Radius of curvature, R = + 3.00 m,
Object-distance, u = – 5.00 m,
Image-distance, v =?
Height of the image, h ′ =?
Focal length, `f=R//2=+(3.00m)/2=+ 1.50m` (as the principal focus of a convex mirror is behind the mirror)
Since `1/v+1/u=1/f`
or, `1/v=1/f-1/u= +1/1.50-1/(-5.00)=1/1.50+1/5.00`
`=(5.00+1.50)/7.50
`v=(+7.50)/6.50= +1.15m`
The image is 1.15 m at the back of the mirror.
Magnification,`m=(h')/h= -v/u= -(1.15 m)/(-5.00 m)`
`= +0.23`
The image is virtual, erect and smaller in size by a factor of 0.23.