Geology Reference
In-Depth Information
Obviously, a value of
n
λ
greater than 1 means slower
velocity of propagation of light.
In isotropic (isometric) crystals the refractive index is
the same for all directions. Light travels at the same veloc-
ity in all directions. This is also the case in isotropic non-
crystalline materials, such as amorphous window glasses
without any thermal tempering or built‐in stresses.
Tempered safety glass used in car windows, however, is
optically anisotropic or birefringent due to the internal
stresses induced by thermal tempering and behaves some-
what like optically positive crystals under compressive
stresses [
Sinha
, 1978a, 1978b]. On the other hand, a crys-
tal of ordinary ice Ih is a naturally birefringent material
and behaves like an optically positive uniaxial crystal
with its optic axis parallel to its
c
axis. The term optically
positive is used to indicate that the ordinary wave, defined
as the wave that travels with the same velocity in all direc-
tions in the crystal, is faster than the extraordinary wave,
defined as the wave whose velocity depends on the direc-
tion of propagation inside the crystal. Both waves are
polarized and are at right angles to each other. However,
both waves travel at the same speed in the direction of the
c
axis and that's the reason for calling the
c
axis also
the optic axis. This axis can be readily visualized as the
line normal to the basal plane or the flat plane of a simple
snowflake shown in Figure 6.3.
To sum up, birefringence is defined as the splitting of a
light wave into two unequally transmitted (or refracted)
waves by an optically anisotropic medium. The degree of
the splitting can be strong or weak depending on the
degree of the geometric order of the crystalline structure.
Some details of the interaction of the incident light in
relation to the crystalline structure of the material can be
found in
Hetcht
[2002].
When a beam of light enters a birefringent material,
the beam is refracted into two beams: ordinary (
O
),
which follows Snell's law, and extraordinary (
E
), which
does not follow the same law. The polarizations of the
two beams are perpendicular. The two incident beams of
which the
O
beam from the first one and the
E
beam
from the second one meet at the same point at the oppo-
site surface. Because of the different path lengths, the two
refracted beams from that side will have different phase
at their meeting point. The interference between these
two refracted waves (constructively or destructively)
determines the amplitude of the departing wave at each
wavelength. Since the amplitude will be different for dif-
ferent wavelengths, the light that exits the crystal will
have a certain color (but not white as the incident light).
The color depends on the phase shift between the ordi-
nary and extraordinary waves at their point of meeting at
the opposite side of the crystal. This phase shift is called
“optical retardation.” This feature makes crystals that
are oriented differently appear in different colors as can
be seen in the photographs of ice thin sections that
appear in this topic. More on this point is presented in
section 6.1.3.
The color of each crystal will be different because it
is determined by three factors: (1) the difference in the
velocity of the two refracted beams in the crystal or the
birefringence denoted by the Greek letter
β
, (2) the orien-
tation of the crystal's optical axis with respect to the inci-
dent light beam, and (3) the thickness of the specimen.
The relationship with the thickness of the specimen is
discussed in the next section.
In ordinary ice Ih, the extraordinary wave is slower than
the ordinary wave. This means that the refractive index
of the extraordinary wave
n
e
(
λ
) is greater than that of the
ordinary wave
n
o
(
λ
) [
Dorsey
, 1940, Table 210, p. 485]. The
term wavelength‐dependent birefringence,
β
λ
, is defined as
nOte On cORneal BiRefRingence
This topic is obviously written to be read by able‐bod-
ied persons visually capable of reading to comprehend
the images of micro‐ , macro‐, and mesoscale remotely
sensed images of ice. It could be of interest to some
of the readers to know that the cornea of human eyes
(like those of most other animals) is also a birefringent
material, like a snowflake, with the optic axis' normal
to the curvature of the eyes or parallel to the direction
of light as its enters the eyes. The epithelium and the
endothelium layers, immediately in the front and the
back of the cornea, however, were shown to be isotro-
pic. These properties of the components of the human
cornea were shown (believed to be for the first time) by
investigating the Rayleigh scattering of linearly polar-
ized coherent beam of laser light, with a wavelength of
632.8 nm, as it travels through the cornea [
Sinha, et al.
,
1968]. This was achieved by using the first successful
He‐Ne gas laser of Canada (developed at the National
Research Council of Canada), which was also used to
investigate stress‐induced Raleigh scattering in tem-
pered glass [
Bateson, et al.
, 1964, 1966]. It is appro-
priate to remember that the first successful laser was
invented in 1963. Polarimetric studies of microwaves
are strongly linked to this type of scattering of EM
waves and hence remote sensing of the future genera-
tions of space‐borne radar sensors.
n
n
(6.1)
e
o
Since
β
λ
is always positive for ordinary ice, its crystals
are known to be optically positive uniaxial. Ih ice is a
weakly birefringent crystal and
β
λ
depends slightly on
wavelength. Its variation (also called dispersion) in the
visible wavelength range can be ignored from all practical
