Graphics Reference
In-Depth Information
where
Δ
y
is a “phase” that depends on our choice of the origin of our coordinate
system. Similarly, the
z
-component must have the form
E
z
(
x
,0,0,
t
)=
A
z
sin
2
t
+Δ
z
.
x
λ
−
c
λ
π
2
π
(26.3)
Inline Exercise 26.3:
Suppose we change units so that the speed of light,
c
,is
1.0; assume that
=
1 as well, and
Δ
z
=
0. Plot
E
z
as a function of
x
when
t
=
0; do so again when
t
=
0.25, 0.5, 0.75, and 1.0.
λ
Physical experiment confirms that the
x
-component of the electric field for a
wave traveling on the
x
-axis is always zero. Thus, the vector
a
=
A
x
A
y
A
z
T
that characterizes the plane wave must always lie in the
yz
-plane;
A
y
and
A
z
can
take on any values, but
A
x
is always zero.
The first important phenomenon associated with the wave nature of light is
diffraction.
Just as waves passing through a gap in a breakwater fan out into a
semicircular pattern, light waves passing through a small slit also fan out. Assum-
ing the slit is aligned with the
y
-axis and the plane waves are moving in the
x
-
direction, the electric field (after the light passes through the slit) will be aligned
with the
y
-direction, that is,
A
z
will be 0.
If we place an imaging plane at some distance from the slit (see Figure 26.7),
a pattern of stripes indicating the wave nature of the light appears.
For the most part, this kind of diffraction effect is not evident in day-to-day
life, but a closely related phenomenon, in which light of different wavelengths
is reflected in different directions by some medium (things like the “eye” of a
peacock feather, or a prism), is quite commonplace.
In studying the electric field associated to light moving in the
x
-direction, we have
a plane wave described by
E
x
(
x
,0,0,
t
)=
0
(26.4)
E
y
(
x
,0,0,
t
)=
A
y
sin
2
t
+Δ
y
x
λ
−
c
λ
π
2
π
(26.5)
E
z
(
x
,0,0,
t
)=
A
z
sin
2
t
+Δ
z
.
x
λ
−
c
λ
π
2
π
(26.6)
The phase constants
Δ
y
and
Δ
z
depend on where we choose the origin in
x
or
t
; if we replace
x
by
x
+
a
, then both
Δ
y
and
Δ
z
will change, but the
difference
between them will remain the same
. This difference can be any value at all (mod
2
π
); in typical light emitted from an incandescent lamp, for instance, all possible
differences between 0 and 2
are equally likely.
The simplest case is a plane wave where
A
y
=
A
z
and
Δ
y
−
π
Δ
z
=
π/
2or
3
2. Such a wave is called
circularly polarized.
If we consider the electric field
of Equation 26.6 at time
t
=
0 and assume that we've adjusted the
x
-axis so that
Δ
y
=
0 and
Δ
z
=
π/
π/
2, the field has the form
