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.

Options

A. 2cm
B. 10cm
C. 8cm
D. 14cm

Answer

b.

Explanation

For part MN,
`u=-30cm, f=-10cm`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)=(1)/(f)-(1)/(u)=(1)/(-10)-(1)/(-30)=-(1)/(10)+(1)/(30)`
`(1)/(v)=(-3+1)/(30)=(-2)/(30)`
`V=-15cm`
`m=(I)/(O)=-(v)/(u)`
`rArr (I)/(O)=-((-15))/((-30))=-(1)/(2)rArrI=5cm`
For image of ST,
`u=-40cm`
`f=-10cm`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/((-40))=(1)/((-10))`
`(1)/(v)=-(1)/(10)+(1)/(40)`
`(1)/(v)=-(-4+1)/(40)=(-3)/(40)`
`=-(40)/(3)cm`
For length of image of ST,
`m=(I)/(O)=-(v)/(u)`
`(I)/(10)=-((-40//3)/(-40))rArr I=-(10)/(3)cm`
Length of image of NT,
`T^(')N^(')=15-(40)/(3)=(5)/(3)cm`
Length of wire in image `=5+(10)/(3)+(5)/(3)=10cm`