Fermat's Principle and Snell's Law

n

1

1.00029

n

2

1.33

n

1

air

n

2

water

Speed	Angle	Time	Product
v 1 = 299 Mm/s	θ 1 = 32.70 deg	t 1 = 3.9650 ns	n 1 sin( θ 1 ) = 0.540
v 2 = 225 Mm/s	θ 2 = 53.63 deg	t 2 = 7.4818 ns	n 2 sin( θ 2 ) = 1.071
		t 1 + t 2 = 11.446879 ns

Fermat's principle states that light travels between two points in such a way that the total time traveled is a minimum. Since light travels at different speeds through different media, the path of least time may not be a straight line. In particular, light travels a longer distance in the medium in which it has a higher speed. You can find the path followed by the light ray by dragging the point on the boundary between the two media so as to minimize the total time

t

1

+

t

2

traveled. At this minimum,

n

1

sin(

θ

1

)=

n

2

sin(

θ

2

)

, as predicted by Snell's law.