The waves produced by this virtual source continue in the same direction they would be going if there was actually a source on the other side of the mirror, which is the angle of reflection. This is why when you look at in a mirror, it looks like you are in the mirror, because it is as if the image of you is a new source that is reflected over the mirror surface (a "virtual" image). The waves do constructively interfere in the air so that its like the source of the wave is reflected over the metal surface (the source looks like it is "inside" the metal). In the case of a metal, these waves destructively interfere inside the metal and so very little of the wave penetrates into the metal. Whenever a light wave is incident on a metal or an insulator like water or glass, each point on the surface radiates a wave that is either 180 degrees out of phase (for a metal or from a low refractive to a high refractive index) or in phase (from a high refractive index to a low index, like from inside glass to air). Ie the quickest path for the photon to travel between these two points is with the same incident and reflected angle, and according to Fermat's principle, that's what they will always do. According to the law of reflection, the angle of incidence equals the angle of reflection.
So if calculate the derivative you will find that the answer looks exactly like incident path: (length of opposite side)/ hypotenuse = reflected path (opposite/hypotenuse) The angle of incidence is the angle between this normal and the incident ray the angle of reflection is the angle between this normal and the reflected ray. Answer (1 of 16): As soon as light falls on the surface of the mirror, it reflects off it in such a manner that angles, theta i & theeta r, formed by coplaner rays, with respect to a perpendicular (normal) to the plane surface, will be equal. If you can find where t is minimal by when the derivative is zero. If surface has a length of 1 and the location where the photon gets reflected is X, A is at height h1, B at height h2, then the time it takes it to go from A to B is, If you start at point A, sometime during the journey reflect of a surface to bounce back to reach point B, then the angle of incident, reflection are completely unknown because you don't know at what point it hits the surface and gets reflected. I remember having to derive this in waves and optics, it's pretty easy to reach the conclusion that the angles mist be the same just with Fermat's principle, which states "the path taken by a ray between two given points is the path that can be traversed in the least time."
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