Geology Reference
In-Depth Information
called
birefringent
meaning two refractive indices or
doubly‐refracting. Birefringence is thus defined as the
splitting of a light wave into two unequally transmitted or
refracted waves by an optically anisotropic medium.
Although water without any applied electric field is
optically isotropic, ordinary ice is doubly refracting, and
this property is responsible for producing beautiful color
in ice thin sections when observed under cross‐polarized
light. It is difficult to provide an unmistakable example of
evidence for the duality of refraction in a single crystal of
ice because ice is a weakly birefringent material with bire-
fringence,
β
, of 0.0014 (to be clarified later) for wave-
length,
λ
, of 546 nm (green). However, an unequivocal
demonstration of double refraction can be made with a
transparent crystal of calcite, popularly known as Iceland
spar with
β
of 0.1738, which is more than two orders of
magnitude (actually 124) greater than that for ice at the
same wavelength of 546 nm. This green color (line) is pre-
dominant in a mercury vapor lamp and close to the maxi-
mum sensitivity of normal human vision. Iceland spar is,
relatively speaking, an exotic material, but chemically it is
calcium carbonate (CaCO
3
) and, therefore, the same as
marble or chalk.
If an object is viewed through a clear cleavage rhombo-
hedron of calcite, two images of the object are seen; one
image is fixed while the other revolves around the fixed
one if the crystal is rotated. This is illustrated in Figure 6.4.
It shows two images of the word “ICE” when a clear
cleaved rhombohedron‐shaped crystal of calcite is placed
over the paper. The triangle at the bottom right corner of
the crystal in Figure 6.4a is cut and polished purposely to
use it as a marker, so that the rotation of the crystal can
be seen without any ambiguity. Note the rotation of one
image around the fixed one as the crystal is revolved
clockwise in steps of 45° through a total angle of 270°.
The top set of letters of the word “ICE” in Figure 6.4a is
the fixed image and the bottom set is the movable image.
The movable set goes above the fixed one when the crystal
is rotated by 180° as can be seen in Figure 6.4e. The fixed
image is produced by the
ordinary ray
whereas the revolv-
ing one is produced by the
extraordinary ray
.
A birefringent material has two velocities of light (elec-
tromagnetic waves in the visible range) or two refractive
indices
n
λ
(
o
)
and
n
λ
(
e
)
depending on the wavelength,
λ
, and
the direction of propagation of light. Here
n
λ
(
o
)
and
n
λ
(
e
)
are, respectively, the refractive indices of the ordinary and
the extraordinary waves to be clarified below. In general,
the refractive index,
n
λ
, for a given wavelength,
λ
, is meas-
ured as the ratio of the speed of light in vacuum,
c
= 2.99792458 × 10
8
m/s) and its speed inside the body. By
virtue of the definition, the value of the refractive index
of vacuum is 1. Because the speed of light is slower inside
a transparent body in comparison to that in vacuum, the
refractive index at any wavelength is greater than 1.
(a)
(b)
(c)
0
45
135
(d)
(e)
(f)
180
270
225
Figure 6.4
Double images of the word “ice” as seen through a rotating clear cleavage rhombohedron of birefrin-
gent (double‐refracting) calcite crystal; note the rotation of one image around the other (fixed one) as the crystal
is revolved clockwise; the angle of rotation is shown at the bottom right corner (photos by N. K. Sinha,
unpublished).
