Physics 458 Problem Set 4 Solutions
Graded Problems
5.3, 5.11, 5.14,5.22, 5.65
5.3)
We are given that for the ellipsoid,
2(
)
ab
(Eq 1).
We need to show that the optical path from F
1
to A to D (where D is on the screen
but at the same distance from the axis as A) is independent of angle.
2
1
1 20
2
1 20
1
2
()
(2
)
2
2
2
path
O
n
n a
x
n v
n
b
a
n v
n
b
a
b
a
a
a
n
a
x
a
x
a
x
(Eq. 2)
We use the law of cosines and the trig relation for x,
2
2
2
(2 )
4
( )
b
b Cos
x
Cos
(Eq. 3)
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View Full DocumentSolving these two equations for
and
, we find
(2
)
1
( )
a b a
a b
Cos
(Eq. 4)
So now we need to show that:
1
2
()
constant
n
a
n
a
x
a
a
Cos
(Eq. 5)
If we substitute Eq. 4 for
this becomes,
1
2
n
ab
a
Cos
a b
n
(Eq. 6)
For any ratio
1
2
n
n
, we can find values of a and b so that Eq. 6 is true and so the light from
F
1
emerges as a plane wave.
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 '10
 HEPPELMANN,STEVEN
 Physics, Orders of magnitude, simple lens

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