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One way to derive the law of reflection, you can use the principle of least action to minimize the action path of motion of light. They key concept while doing this is to take the derivative of the time the light takes to go from one point to the another, then setting this derivative to zero. Say the notation is dt/dx, this means that the infinitesimal change in time over the infinitesimal change in position is equal to zero. What is the meaning of dt/dx in non-mathematical terms?

Thanks.

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  • $\begingroup$ Comment to the post (v1): Did you mean to use Fermat's principle rather than the principle of least action? $\endgroup$ – Qmechanic Mar 9 '16 at 20:43
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It means that while trying a continuous family of pathes parameterized by a scalar u (works also for 2 or 3 coordinates) and measuring their length and duration T, the solution corresponds to the minimum duration, which is find at dT/du=0.

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