The image of an object formed by a mirror is real, inverted and is of magnification - 1. If the image is at the distance of 30 cm from the mirror.
(i) Where is the object placed ?
(ii) Find the position of the image object is now moved 20 cm towards the mirror.
(iii) What is the nature of the image obtained ? Justify your answer with the help of ray diagram.

Explanation

Image of an object formed by a mirror is real, inverted indicates that the mirror is a concave mirror and that the image is formed on the same side as the object.
(i) `m=-1 , v=-30 cm`
`m =-(v)/(u)`
`-l=-((-30)/(u)), u=-30` cm is the object distance
(ii) Find focal length of the concave mirror using data from 1.
`(1)/(v)=(1)/(u)=(1)/(f)`
`(1)/((-30))+(1)/((-30))=(1)/(f), f=-15 cm`
`u=-10 cm , f=-15 cm, v = ?`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/((-10))=(1)/((-15)), v = +30 cm`
The + sign indicates that the image is formed behind the concave mirror
(iii) `m=-(v)/(u)`
`m=-((30)/(-10)), m = 3`
The image is erect, virtual and enlarged