Fermat

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Red Man

Blue Man

and Green Man

are having an argument. They have to run a race from point 1 to point 2 over concrete and then soft sand. They can each run at 9 m/s on the concrete but only 5.2 m/s in the sand.

Red Man says "You need to maximize the distance over the concrete surface. You should run to the boundary point above point 2 and then run straight down."

Green Man says "Nonsense! You should minimize the distance. Run straight to point 2."

Blue Man (being a New Age type of guy) says "Nada. You must follow the path of light"

Fermat's Principle states that light travels from point 1 to point 2 in the least possible time. This gives rise to snell's law of refraction for light:
v₂sin(q₁)= v₁sin(q₂)
where q₁ is the angle of incidence (with the perpendicular) at a surface , q₂ is the angle of refraction in the material, such as, glass, on the other side of the surface. Actually this law applies to all waves going from 1 medium to another where the speed changes, such as, water waves entering shallow water. The application below is designed to help you understand this.

You are runner whose task it is to run from point 1 to point 2 in the shortest possible time.

Click on each man to line them up at the start.
Click anywhere to start the race.
Click anywhere to line them up for a new race.