If you are curious, you have probably noticed a strange curve in your breakfast bowl. You can reproduce it by placing a ring on your hand or on the floor. Try it: once seen, never forgotten! It soon becomes clear that this phenomenon is created when light rays reflect off a circle, but… what is this curve? Can we determine its equation and properties?
When rays come into focus
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The family of light rays reflected off a circle is easy to study. We draw the rays coming from the sun, followed by the rays reflected off the circle. The relationship between them is simple: the incoming and reflected rays make equal angles with the normal to the circle at the point of incidence. Taking the line pointing toward the sun as the x-axis gives the following diagram.
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