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

`R=20 cm, f=R=-10 cm `
For part `AB_1PB=30+10=40cm`
so, `1/v=-1/f-1/u`
`=1/10-1/(-40)=3/40`
`rarr v=(-40)/3=13.3cm`
So, `PB'=13.3cm`
`m=(A_1B_1)/(AB)=-(-(v))/u`
`=(-(-13.3))/40=(-1)/(-3)`
`rarr A_1B_1=10/3=3.33cm`
for part CD, PC=30`
so `u=-30 cm `
`1/v=1/f-1/u`
`=1/10-1/(-30)=1/2`
`rarr v=-15cm=PC'`
`m=(C_1D_1)/(CD)=-v/u`
`=-((-15))/30=-1/2`
`rarr C_1D_1=5cm`
`rarr B_1C-1=PC_1-PB_1`
`=15-13.3=1.7cm`
So, total length `A_1B_1+B_1C_1+C_1D_1`
`=(3.3)+(1.7)+5=10cm`