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In ancient Greece it was known that parabolic mirrors, which are paraboloids of revolution, have the property of concentrating parallel rays towards the axis of symmetry at the focal point of the paraboloid. It is said that this property was used by Archimedes to burn enemy ships. Spherical mirrors do not exactly possess this property, but they manage an approximation, that is, the reflections of the rays which go parallel to the axis of a spherical mirror very near to the vertex pass very near the focal point. According to the equation of the mirror they would pass exactly through the focal point, but remember that this equation is just an approximation. The following visual illustrates this phenomenon. You can modify the radius of the mirror and its width (clicking on and dragging the red dots). When can you get the majority of rays to pass through the focal point? |
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