Physics Of Physics Regarding Light Rays

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I have always been interested in the way light travels, not just in how, but also in all the other factors that affect the light rays, including the speed, the velocity, the distance, as well as others. In my past years of school, I had been able to explore areas of physics concerning light rays, as part of my physics course. However, I had previously only learned the basic principles, such as the laws of refraction and reflection. Because I chose to focus on Chemistry and Biology, I was not given the opportunity to delve deeper into the subject, and had only obtained basic understanding of it. Although I knew of the principles and what they represented, I did not become fully aware of the fact that the principles were based off of…show more content…
For example, we want the light to bounce off a mirror or to pass through a piece of glass on its way from A to B. Fermat 's principle states that of all the possible paths the light might take, that satisfy those boundary conditions, light takes the path which requires the shortest time.
(A more accurate statement of Fermat’s principle: Any hypothetical small change in the actual path of a light ray would only result in a second order change in the optical path length. The first order change in the optical path length would be zero.)
Consider the diagram on the right. We want light to leave point A, bounce off the mirror, and get to point B. Let the perpendicular distance from the mirror of both A and B be d and the shortest distance between the points be D. Assume that light takes the path shown. The length of this path is then:

Since the speed of light is the same everywhere along all possible paths, the shortest path requires the shortest time. To find the shortest path, I differentiated L with respect to x and set the result equal to zero. (I did this in order to yield an extremum/minimum in the function or the derivative of L(x).) And thus obtained the value of the least amount of time.

After canceling equal terms on both sides I was left with:

or

The path that takes the shortest time is the one for which x=D/2, or equivalently, the one
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