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Arnold's Trivium
1991 Arnold's Trivium
19
Problem 19
Problem 19
Source:
July 1, 2010
trigonometry
Problem Statement
Investigate the path of a light ray in a plane medium with refractive index
n
(
y
)
=
y
4
−
y
2
+
1
n(y)=y^4-y^2+1
n
(
y
)
=
y
4
−
y
2
+
1
using Snell's law
n
(
y
)
sin
α
=
const
n(y)\sin\alpha = \text{const}
n
(
y
)
sin
α
=
const
, where
α
\alpha
α
is the angle made by the ray with the
y
y
y
-axis.
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