Why is the parabolic disc antenna and how is it connected with Fermat's law?

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Why is the parabolic disc antenna and how is it connected with Fermat's law?

According to Fermat's theorem, a ray follows the direction that takes the least amount of time, and occurs only when the angle of incidence is identical to the angle of reflection or propagation. The rays of light (EM-waves) travel the direction of stationary optical length, according to Fermat's theory (principle of least time).

Dish antennas are typically parabolic so that they can combine all incoming signals to increase their strength. Incoming signals are particularly weak for dish TV antennas. So we use parabolic antennas to add up many identical signals at the focus point. The above structure of a parabolic antenna suggests that all rays have nearly the same length (or take the least amount of time as per fermat's principle) to reach the focus point.

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