Page 143 - Fundamentals of Light Microscopy and Electronic Imaging

126 PROPERTIES OF POLARIZED LIGHT

Demonstration: Double Refraction by a Calcite Crystal

• Place a crystal on a page of printed text and rotate the crystal while looking
down on it from above. One ray does not move as the crystal is rotated (the
O ray), whereas the other ray (the E ray) rotates around the fixed ray accord-
ing to the angle of rotation of the crystal (Fig. 8-6). The O ray does not move
because it obeys the laws of normal refraction and passes through the crystal
on a straight, undeviated trajectory. The E ray, in contrast, travels along a
tilted or oblique path, and its point of emergence at the surface of the crystal
changes depending on the orientation of atoms in the crystal and therefore on
the orientation of the crystal itself. Because the angle of divergence is so
great, wedges of calcite crystal can be cut and glued together in such a way
that one of the two components is reflected and removed while the other is
transmitted, making calcite an ideal linear polarizer.
• Examine the crystal resting on a black spot on a blank page through a
dichroic polarizing filter held close to the eye, while rotating the crystal
through 360°. First one ray and then the other ray alternately comes into view
and becomes extinguished, and the black spot appears to jump back and forth
as the filter is rotated through increments of 90°. The double images corre-
spond to the O and E rays, each of which is linearly polarized and vibrates in
a plane perpendicular to the other. For most crystals the two rays are close
together and must be magnified to be observed, but in calcite the rays are so
widely separated that no magnification is necessary. As we will see, this is
due to large differences in the refractive index along different paths through
the crystal. Notice too that polarized light cannot be distinguished from ordi-
nary random light and that an analyzer is required to distinguish the different
planes of polarization.

Materials such as calcite, quartz, and most molecularly ordered biological struc-
tures that contain a single optic axis are called uniaxial. Another class of biaxial crystals
with two optic axes also exists, but is rarely encountered in biological systems. Biolog-
ical examples of ordered macromolecular assemblies that can be seen in the polarizing
microscope include such objects as lipid bilayers, bundles of microtubules and actin fil-
aments, plant cell walls, crystalline granules of starch, lignin, and other materials, chro-
mosomes from certain organisms, DNA kinetoplasts in trypanosomes, chloroplasts, and
many other structures.
We have used the terms double refraction and birefringence to refer to the ability of
molecularly ordered objects to split an incident ray of light into two components, the O
and E rays, but the two terms refer to different aspects of the same process. Double
refraction refers to the visible phenomenon: the splitting of a single incident ray into two
resultant rays as exemplified by a crystal of calcite. Birefringence refers to the cause of
the splitting: the existence of direction-dependent variation in the refractive index in a
molecularly ordered material. Birefringence B also refers to a measurable quantity, the
difference in the refractive index (n n ) experienced by the O and E rays during tran-
e
o
sit through an ordered object such that
B (n n ).
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e