Phys 375 HW 2
Fall 2010
Due 20 September, 2010
1
.
Pedrotti
3
, 3
rd
edition, problem 27 (see Fig. 233).
Solution:
See FIGURE 233in the text P
3
From the geometry it is clear that
h
D
C
4
/
tan
=
θ
, where h is the height of the slab
and D is the diameter of the circle of light.
From Snell’s law we know that the critical
angle occurs when the angle of refraction is
2
π
θ
=
R
.
Then applying Snell’s Law,
2
2
1
1
sin
sin
θ
θ
n
n
=
we have:
(
)
55
.
1
4
/
4
/
sin
2
/
sin
2
2
=
+
=
=
h
D
D
n
n
C
air
glass
θ
π
Where I used
1
=
air
n
.
2
.
Write an expression for the
E
 and
B
fields that constitute a plane harmonic wave
traveling in the +
z
direction.
The wave is linearly polarized with its plane of vibration at
45
o
to the
yz
plane.
Solution:
For a plane wave traveling in the +zdirection we know the functional form of the
wave must be
(
)
t
kz
ω
−
sin
or cosine.
Since the wave is traveling in free space, it must be
transverse.
This implies that
0
=
z
E
.
For light polarized linearly at a 45° the normalized
polarization vector is
(
)
y
x
ˆ
ˆ
2
1
+
.
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 Spring '11
 ENO
 Physics, Light, Snell's Law, Total internal reflection

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