Question

A U-shaped wire is placed before a concave mirror having radius of curvature 20cm as shown in figure (18-E1). Find the total length of the image.​

Answer 1

Given :

R= 20cm

f= R/2 = 20/2 = 10cm

For part AB, PB =u= 30+ 10 = 40cm

so  u= - 40cm

1/v+1/u=/1f

1/v= 1/f- 1/u

= -1/10 + 1/40

= - 4+1/40

v= - 40/3 = -1 3.3cm=

m= -v/u = -(-13.3)/ -40 = -1/3

 hi/ho= m

hi= mx ho=-10/3  = - 3.33cm

For part CD, Pc= 30

u= -30cm

1/v=1/f-1/u = 1/10 +1/30 = - 2/30

v= - 15cm= Pc'

m= C1D1/CD = - v/u = -(-15)/30 = -1/2

C1D1= 5cm

B1C1=Pc1- Pb1= 15- 13.3 = 1.7cm

so total length is A1B1+B1C1+ C1D1= 3.3 +1.7 +5= 10cm