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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:
n1sin(q1)= n2sin(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, n1 and n2 are the indices of refraction above and below the surface, respectively. For light the index of refraction is c/v where c is the speed of light in a vacuum and v is the speed in the material in question. 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. The gray area is concrete on which you can run at 9 m/s and the brown area is soft sand on which you can run at 5.2 m/s.
Click and drag the transparent protractor to the point at which you think you should cross the border and release the mouse button. Click on the time button to find your transit time in seconds. Readjust your crossing point until you find the minimum time which is 52 seconds. When you find it, Feedback will be given in the Text Area below.