An object is placed (i)`10 cm` (ii) `5 cm` in front of a convex mirror of radius of curvature `15 cm`. Find the position, nature and magnification of the image in each case.

Explanation

The focal length f=`-15/2` cm = `-7.5cm`
i) The object distance u=`-10cm`. Then
`1/v+1/(-10)= 1/(-7.5)`
or `v=(10 xx 7.5)/(-2.5)=-30cm`.
The image is 30cm from the mirror on the same side as the object.
Also, magnificaton `m=-v/u=-(-30)/(-10)=-3`
the image is magnified, real and inverted.
ii) the oject distance u=`-5cm`. Then
`1/v+1/(-5)= 1/(-7.5)`
or `v=(5 xx 7.5)/(7.5-5) = 15cm`.
The image is formemd at 15cm behind the mirror. It is virtual image.
Magnification `m=-v/u=15/-5=3`
The image is magnified, virtual and erect