A U-shaped wire is placed before a concave mirror having radius of curvature 20cm as shown in figure,. Find the total length of the image.

Explanation

Image of AB:
`u=-40cm,f=-(20)/(2)=-10cm,v=?`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(v)+(1)/(-40)=(1)/(-10)`
`(1)/(v)=-(1)/(10)+(1)/(40)=(-4+1)/(40)`
`v=-(40)/(3)`cm
`(I)/(O)=-(v)/(u)`
`(I)/(10)=((-40)/(3))/(-40)`
`I=(-10)/(3)cm`
Image of `CD:u=-30cm,f=-10cm, v=?`
`(1)/(v)+(1)/(-30)=(1)/(-10)`
`(1)/(v)=-(1)/(10)+(1)/(30)=(-3+1)/(30)`
`v=-15cm`
`(I)/(O)=-(v)/(u)`
`(I)/(10)=-(-15)/(-30)`
`I=-5cm`
Total length of image
`=A^(')B^(')+B^(')C^(')+C^(')D^(')`
`=(10)/(3)+(15-(40)/(3))+5`
`=10cm`