Laboratory Techniques for Revealing the Structure of Polycrystalline Ice - Sea Ice: Physics and Remote Sensing - page 238

points of view. For ordinary ice with n e = 1.3104 and n o =
1.3090 from Dorsey [1940, Table 210, p. 485] at −3 °C,
β λ = 0.0014 for the middle of the visible range, i.e., the
orange D line from a sodium vapor lamp with λ =589.3 nm
or the corresponding wave number (defined as 1/ λ ) of
16,969.3/cm. This is one of the lowest values among
those of most minerals. As mentioned earlier, calcite
crystal with β = 0.1738 is 124 times stronger than ice. For
calcite, n o = 1.6618 and n e = 1.4880 for λ =546.

The phase shift does not alter the wavelength, and
thereby the color will remain the same as that of the
wavelength chosen monochromatic light. Only the bright-
ness will be affected because it depends on the phase shift.
The maximum brightness will be for the thickness that
introduces a phase shift of λ /2, for which the two waves
will combine to produce a new wave having the sum of
their amplitudes. An opposite effect will occur if the
phase shift is λ and the crystal will appear as dark. The
crystal will have intermediate brightness for intermedi-
ate phase shift, for example, a phase shift of λ /4. Thus,
the brightness will vary from darkness for retardation of
( nλ ) and maximum intensity for optical retardation, R of
(2 n + 1)/2 λ . The number n takes values 1, 2, 3, etc., and is
called the order of interference. The relative optical retar-
dation, R λ depends on the wavelength, λ , and is related to
the birefringence, β λ , according to

6.1.3. Optical Retardation

If a simple flat snowflake or a section cut parallel
to the basal plane (i.e., perpendicular to the c axis) of
an ice crystal is examined between crossed polarizers, it
remains black irrespective of rotation, as pointed out in
Figure 6.3. However, if thin plates or sections of poly-
crystalline ice (e.g., c axis of the crystals randomly ori-
ented) are examined between crossed polarizers using
white light as the source of illumination, then wonderful
color effects would result. Each crystal in a thin section
appears to have different colors and the plate becomes a
mosaic of colors. The special effects are due to proper-
ties of light known as interference in waves and the
results are known as interference colors. The effects are
very complex but predictable. However, it requires an
understanding of the physics that governs the passage of
polarized light with a wide range of wavelength (such as
white light) through doubly refracting crystals. This will
be described below, but first the effects on monochro-
matic light of a single frequency or wavelength, λ , will be
explored.
The passage of light through a single crystal of ice
can be visualized using the electromagnetic theory of
light. In case of a plane‐polarized monochromatic (single
wavelength, λ ) beam of light traveling through a single
crystal of ordinary ice, the electric vector may be assumed
to have broken up into two components, one as the ordi-
nary wave perpendicular to the c axis and the extraordi-
nary wave along the c axis. These two waves will emerge
from the ice crystal with a shift in phase because they will
travel at different velocities. This phase difference is
called optical retardation. The phase shift depends on
the thickness of the ice crystal and its crystallographic
orientation with respect to the direction of propagation
of the light beam and its plane of polarization. If the
analyzer is set in the position of extinction with respect
to the polarizer, i.e., in the “cross position,” as illustrated
in Figure 6.3, the ice crystal, with its c axis not parallel to
the direction of propagation, will appear as brighter,
depending on thickness, when viewed through the ana-
lyzer. The intensity will actually vary from darkness to
the maximum brightness depending on the thickness of
the crystal.

Rn n t t (6.2)

e o

where t is the thickness of the single‐crystal ice plate,
measured normal to the c axis. For oblique incidences,
considerations have to be given to the crystallographic
alignment of the crystal with respect to the direction of
polarization and propagation of light, hence the equiva-
lent optical thickness along the basal plane or normal to
the c axis.
For the purpose of simple illustrations applicable to
most minerals, for which the dispersion may not be
neglected, it is suitable to calculate the dependence of opti-
cal retardation on crystal thickness using the birefringence
of light with a wavelength somewhat in the middle of the
visible range, 400-800 nm. A convenient wavelength for
most minerals is that of the orange colored, readily avail-
able sodium D line (589.3 nm). This is the dominant radi-
ation from the sodium lamp and the predominant color
of the fluorescence bulbs or tubes of streetlights used
these days. For this wavelength , as shown earlier, the bire-
fringence of ice at −3 °C is β λ = 0.0014. Calculated results
according to equation (6.2) and β λ = 0.0014 are shown in
Figure 6.5. Unlike most minerals, fortuitously, the birefrin-
gence of ice Ih is very low, and more importantly its dis-
persion within the visible range is practically negligible. In
the visible spectral range 486.1-706.5 nm the birefringence
has a constant value of 0.0014 [ Dorsey , 1940, Table 210,
p. 485]. Its value at the lower end of the visible range, at
404.6 and 435.8 nm, is only marginally larger at 0.0015 [see
also Hobbs , 1974, Chapter 3]. This allows the line depicting
the dependence of retardation versus thickness in Figure 6.5
as practically universal for ice in the visible range.
When a single crystal is viewed through cross polar-
ized, its color will be black for all wavelengths when the
thickness is zero. As the thickness increases, the crystal