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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.
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