An example in which reflection in the unit circle sends a ve

An example in which reflection in the unit circle sends a vertical line to a semicircle is shown in Figure 8.5. Figure 8.5: Reflection of the line x = 1 Give intuitive reasons why the reflection of the line x = 1 in the unit circle should have one end at 1 on the x-axis and the other end at O. Show that the line x = 1 has equation z+z = 2, and that its reflection in the unit circle has equation w + w = 2ww.

Solution

8.4.1

The more we move in vertical direction along the line x = 1 more we go away from the circle and hence image should also be formed away from the circle . So, it takes the shape of circle.

The image (circle) and line virtually start from the same point because the distance between the object and the mirror is neglegible.