Find
the fastest Path
Related java applet
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
L1
where index of refraction n1 = c / v1,
This is also true for other waves (e.g.
sound wave) propagation between two different medium.
Your suggestions are highly appreciated!
E-mail : Please click hwang@phy03.phy.ntnu.edu.tw
!
Author¡GFu-Kwun Hwnag Dept. of Physics National Taiwan Normal Univ.
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