Biomedical Engineering Reference
In-Depth Information
Solution
Rearranging the preceding equations,
998*10
∧
8
25*10
∧
8m
c
tissue
¼
c
0
=
n
tissue
'
(2
:
Þ=
1
:
33
¼
2
:
=
s for clear tissue
while
998*10
∧
8
00*10
∧
8m
c
glass
¼
c
0
=
n
glass
'
(2
:
Þ=
1
:
5
¼
2
:
=
s for glass
The significance of this result is that light travels faster through a material with a lower index
of refraction, such as clear tissue (e.g., cornea, aqueous humor, and lens of the eye), compared
to glass. This has many implications as you will see later in this chapter when it comes to deter-
mining the angle of reflection and refraction of light through differing materials and clear tissues.
The intensity or power per unit area of the wave can also be expressed in terms of the Poynt-
ing vector,
—that is, defined in terms of the vector product of the electric andmagnetic field as
P
P ¼
E
H
ð
17
:
8
Þ
The intensity of the wave is the average value of the Poynting vector over one period of the
wave, so if E and H are spatially orthogonal and in phase, as shown in Figure 17.1, then
E
2
I
¼ < P > ¼
power
=
unit area
¼
c
e
ð
17
:
9
Þ
where
. For this equation it is clear that the intensity
is proportional to the square of the electric field. This is true for the propagation of a wave
through an isotropic dielectric medium. From Maxwell's equations it can be shown that the
intensity is also proportional to the square of the magnetic field. Therefore, if the electric
and magnetic fields were in phase quadrature (90 degrees out of phase), then the intensity
would be zero, as shown following
<
P
>
represents the average value of
P
¼< P >¼<
E
o
cos (
o
t
Þ
H
o
sin (
o
t
Þ >¼
0
ð
17
:
10
Þ
I
since the average value of a sine wave times a cosine wave is zero.
In addition to intensity, light can be characterized by its wavelength or, rather, electro-
magnetic spectrum, which ranges from low-frequency radio waves at 10
3
Hz to Gamma
radiation at 10
20
Hz. As depicted in Figure 17.2, the wavelength region of light can be
divided into ultraviolet, which is 0.003 to 0.4 micrometers, to the visible region of 0.4 to
0.7 micrometers (7.5
10
14
Hz frequency range), to the near infrared region
of 0.7 to 2.5 micrometers, to the mid-infrared region of 2.5 to 12 microns, and to the far
infrared beyond 12 microns.
10
14
to 4.3
17.1.2 Optical Polarization
In the previous section the sinusoidal solution in terms of E
x
and H
y
is only one of an
infinite number of such sinusoidal solutions to Maxwell's equations. The general solution
for a sinusoid with angular frequency
o
can be written as
E
(
r
,t
Þ¼
E
(
r
Þ
exp (j
o
t
Þ
ð
17
:
11
Þ
in which
E
(
r
,t) and
E
(
r
) are complex vectors and
r
is a real radius vector.
