How Does Light Reflect in an Ellipse to Connect Its Foci?

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Light reflecting in an ellipse demonstrates that a ray originating from one focus will reflect off the ellipse's surface and pass through the other focus. This phenomenon is explained using the principle that the angle of incidence equals the angle of reflection (i = r), rather than Fermat's principle. The discussion also touches on the relationship between the length of segment d2 and the distance between the foci, which is 2*c. Understanding this relationship is crucial for grasping the reflective properties of ellipses. The reflection property of ellipses has significant implications in various fields, including optics and astronomy.
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I needed the proof of this:if a ray of light passes from one focus of an elipse after reflection it will pass the other focus.please i need the one only using the fact that i=r ( not the fermat rule)
 
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In reference to the attached image, what do you know about length of segment d2 compared to the distance 2*c between the foci?
541px-Ellipse_derivation_1.svg.png
 
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