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49. Let
θ
be the angle of incidence and
θ
2
be the angle of refraction at the left face of the plate. Let
n
be the
index of refraction of the glass. Then, the law of refraction yields sin
θ
=
n
sin
θ
2
. The angle of incidence
at the right face is also
θ
2
.I
f
θ
3
is the angle of emergence there, then
n
sin
θ
2
= sin
θ
3
. Thus sin
θ
3
= sin
θ
and
θ
3
=
θ
. The emerging ray is parallel to the incident ray. We wish to derive an expression for
x
in
terms of
θ
.I
f
D
is the length of the ray in the glass, then
D
cos
θ
2
=
t
and
D
=
t/
cos
θ
2
. The angle
α
in the diagram equals
θ
−
θ
2
and
x
=
D
sin
α
=
D
sin(
θ
−
θ
2
). Thus
x
=
t
sin(
θ
−
θ
2
)
cos
θ
2
.
If all the angles
θ
,
θ
2
,
θ
3
,and
θ
−
θ
2
are small and measured in radians, then sin
θ
≈
θ
, sin
θ
2
≈
θ
2
,
sin(
θ
−
θ
2
)
≈
θ
−
θ
2
,andcos
θ
2
≈
1. Thus
x
≈
t
(
θ
−
θ
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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