Reflection, Time, and the Law of Reflection

In the previous simulation, we looked at how light reflects from a plane mirror in such a way as to minimize the travel time from the red point to the purple point (but going via the mirror). In this simulation, we look at the connection between the minimization of the travel time and the law of reflection.

It turns out that the law of reflection is completely consistent with light taking the minimum time to travel from one point to another, via the mirror. Comparing the two graphs (perhaps aided by the numerical readout of the total travel time), you should be able to see that the minimum travel time corresponds to the situation in which the angle of incidence equals the angle of reflection (and that's the law of reflection).

Let's say you have two points, and you want light to travel from one point to the other, bouncing off a plane mirror along the way. In this simulation, the first point is colored red and the other point is colored purple.

Set the positions of points 1 (red) and 2 (purple) by clicking-and-dragging them to the positions you want them to be in air. Then, click-and-drag the third point (colored green in the simulation) that is on the mirror - this sets the point on the mirror the light reflects from on its way from point 1 to point 2.

Your goal is to adjust the position of the point on the mirror so that the light takes the smallest possible time to travel from point 1 to point 2, and then you have to think about how this relates to reality. In other words, which of the many possible paths the light could take does the light actually take?

Simulation first posted on 3-6-2017. Written by Andrew Duffy. Idea from Dan MacIsaac.

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This work by Andrew Duffy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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