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

10 cm

U shaped wire is placed on the principle axis of the

mirror. The two sides of the U-shaped wire will form image because they are vertical to the principle axis, i.e. AB and CD. The BC side of the wire not form any image. Hence, we can consider the U-shaped wire as the two wires AB and CD

The height of the wire AB, h = 10cm

Radius of curvature, R = 20cm

According to the diagram

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

So the distance of AB from the mirror, u = -40cm

Using mirror formula,

Hence, the image of AB side of the wire is formed at 13.3cm away from the mirror as shown in the figure

Magnification m=

Height of the image formed= -10/3 = -3.33 cm

The negative sign represents the inverted image.

Similarly, for the CD part of the wire

PC= 30cm, hence. u= -30cm

Hence, the image of CD side of the wire is formed at 15 cm away from the mirror.

Height of the image formed= -10/2 = 5 cm

B’C’= PC’- PB’ = 15 -13.3 cm = 1.7cm

Hence total length A’B’ + B’C’ + C’D’ = 3.3 +1.7 + 5 =10cm