Activities
The positions of the points on the screen are specified
in meters - if you right-click on any point on the screen, the
coordinates of that point will show up in yellow in the bottom left of
medium 2 (the lower medium). The travel times for light over the various
paths are given in nanoseconds - light is very fast!
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When you first start the simulation, the three points are all along a
vertical straight line. Without moving the points, adjust the index of
refraction of each medium. What effect does this have on the travel
time for the light? What does this tell you about the connection
between the index of refraction of a medium and the speed at which
light travels in that medium?
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Now, look at the graph (the graph of light travel time as a function
of the position of the point the light passes through on the interface
between the two media) as you click and drag the green point left and
right. Determine where the green point has to be to minimize the time
it takes for light to travel from point 1 (red) to point 2 (purple).
Explain why this location for the green point makes sense.
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Now, click and drag point 1 (red) to a location in the upper left of
medium 1, and move point 2 (purple) to a location in the lower right
of medium 2. Once again, move the green point left and right to
determine the path the light follows from point 1 to point 2 that
minimizes the travel time. Try this in three different situations: (a)
when the two media have the same index of refraction, (b) when medium
1 has a higher index of refraction than medium 2, and (c) when medium
1 has a lower index of refraction than medium 2. Is the minimum-time
path also the minimum-distance path? Explain.
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It turns out, when light travels from a point in one medium to a point
in another medium, that it actually follows the path that minimizes
the travel time. Based on your investigations with this simulation,
what are some implications of that?