cabin in the Ontario wilderness. One evening, Ahmed and Mihai miss teaching so
much that they leave the cabin for a math adventure. They go to the nearby lake
equipped with a powerful flashlight, a small mirror, a calculator, and a protractor.
The water is still so they can see the reflection of everything in the moonlight.
Mihai and Ahmed decide they want to find out the width of the lake so they stand
at opposite edges of it. Ahmed holds up the mirror just above his head. With the
flashlight near the top of his head, Mihai carefully points it to a spot on the lake
directly between them so that the beam reflects off the lake onto Ahmed's mirror.
They know that the physics of light relies on three crucial principles:
i) Light travels on the path that minimizes the travel time.
ii) The shortest path between two points is a line segment between them.
iii) The speed of light is constant.
By measuring the angle at which Mihai's flashlight is pointed, how can they deter-
mine the width of the lake using these 3 principles? As always, justify your answer.
Note: Do not use any other physical principles of light unless you mathematically
justify them from those written above.
Hint: First, you must give a formula for the width of the lake which will depend
on several constants that Ahmed and Mihai can determine (or should obviously
already know) without any extra tools. Second, you must use calculus to justify this
formula using the principles described above. If you do not use calculus and all three
principles, you are probably missing something.