Graphics Reference
In-Depth Information
Figure 26.6: Ocean waves arriving at Panama City. The waves come in long lines, which
have been slightly bent by the irregularities of the ocean floor as they approach the shore.
(Courtesy of Nick Kocharhook.)
surface: As waves pass, the log rises and falls, and may also move somewhat back
and forth in the direction of the wave, but long after the peak of the wave has
moved on, the log remains more or less where it started.
Inline Exercise 26.2:
(a) A thin human hair has a diameter of 50
μ
m
≈
1
500
inch. Red light has a wavelength of about 700 nm. How many red wave-
lengths is one hair diameter?
(b)
Diffraction
is an effect that typically occurs when a wave phenomenon
interacts with an object whose scale is about the same order of magnitude as
the wavelength of the wave. Do you expect to see diffractive effects in the
interaction of human hair and visible light?
A basic electromagnetic wave moving through space is a
planar wave.
Just
as an ocean wave has a height at each point of the ocean surface, a light wave has
an electric field at each point of space. And just as the heights of the ocean wave
are the same all along a ridge line or a trough line, the electric field is the same
all along a
plane
(at least within some large enough radius that this is a decent
approximation). This means that we can describe the plane wave by describing its
values along a single line perpendicular to that plane. For instance, if the wave is
constant along planes perpendicular to the
x
-axis, then we can know, at each time
t
, its value at a point
(
x
,
y
,
z
)
by knowing its value at
(
x
,0,0
)
:
E
(
x
,
y
,
z
,
t
)=
E
(
x
,0,0,
t
)
.
The velocity with which the peaks of the wave move along the
x
-axis is
c
,the
speed of light, and the wave shape is sinusoidal. This means that the expression
for, say, the
y
-component of the wave must have the form
E
y
(
x
,0,0,
t
)=
A
y
sin
2
ft
+Δ
y
x
λ
−
π
2
π
(26.1)
=
A
y
sin
2
t
+Δ
y
,
x
λ
−
c
λ
π
2
π
(26.2)
