Find the fastest Path

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In the above java applet, there are two different regions (green and yellow).

The condition is :

An object (red) located at the top left corner of the green region.

It is going to move to the bottom right corner of the yellow region.

Due to different friction in these two regions,

its speed is also different (green: V1 , yellow: V2)

You can change value of V1 and V2 from the textfield.

How to chose a path such that minimizes the travel time?

Those two arrors represent the velocity vectors at those two region.

You can click the left mouse button at the tip of the velocity vector

and drag it left and right, to change the traveling path.

To make it more interested. You can click the mouse button at the boundary,

and drag it up and down, to change the height of those two regions.

Press Start button to start the animation.

A red ball will move along the chosed path.

Another ball(blue) will follow the fastest path if you click the show checkbox:

When it stop, compare the ratio of L1/L2 and compare with V1/V2

Did you get the right answer?After how many tries?

Sounds familar? Fermat's principle states that:

The path of a ray of light between two points is the path that minimizes the travel time.

We can derives Snell's law from the relation found above

where index of refraction n₁ = c / v₁_,

c is the speed of light in vacuum, and

v₁

is the speed of light in the medium.

This is also true for other waves (e.g. sound wave) propagation between two different medium.

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