An object is placed at a distance of 25cm from a concave mirror and a real image is formed by the mirror at a distance of 37.5cm What is the length of the mirror? Now if the object is moved 15cm towards the mirror, what will be the image distance, its nature and magnification ?

Explanation

`"Here," u=-25 cm , v=-37.5 cm`
`"We know", (1)/(f)+(1)/(u)=(1)/(f) or, (1)/(-37.5)+(1)/(-25)=(1)/(f)`
`or, " " (1)/(f)=-(10)/(375)-(1)/(25)=-(25)/(375)=-(1)/(15) or, f=-15 cm`
Now if the object is moved 15 cm towards the mirror, the object distance will be `-(25-15)=-10 cm`
`therefore " " (1)/(v)+(1)/(-10)=-(1)/(15) or, (1)/(v)=-(1)/(15)+(1)/(10)=(-2+3)/(30)=+(1)/(30)`
The positive sign of vindicates that the image formed by mirror is virtual and it is formed at a distance of f30 cm behind the mirror.
`"Magnification",m=-(v)/(u)=-(30)/(-10)=3`
`therefore` The image will be magnified 3 times. The positive sign of m indicates the images as erect.