A ray of light goes from point A in a medium in which the speed of light is v
1
to point V
in a medium in which the speed of light is v
2
.
1. What is the time required to go from A to B ?
2.
Show that the time reaches its minimum
when n
1
sin
T
1
=n
2
sin
T
2
(so that the actual path the light takes
minimizes traveling time!)
Solution
A. The time requires is given by the distances divided by corresponding velocities
2
2
2
2
1
2
1
2
x
h
l
h
t
v
v
±
±
±
B. Consider arbitrary path.
Then the time needed is given by
2
2
2
2
1
2
1
2
(
)
(
)
( )
x
z
h
l
z
h
t z
v
v
±
±
²
±
±
Let us consider this as a function of deviation
z
and require
to find such
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 Fall '09
 RichardScalettar
 Light, Sin, 2 L, v1 v2

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