A U-shaped wire is placed before a concave having radius of curvature 20 cm as shown (18-E1). 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`