Physics for Geologists, Second edition

Optics 49
Figure 4.4 Polarizer (P) and analyser (A) crossed, and inclined. Light coming
from below (from the other side of the paper, as it were) passes first
through the polarizer, which polarizes the light parallel to its princi-
pal axis PP. This polarized light cannot pass through another crystal
with its principal axis normal to the polarizer (on left in diagram).
At other angles, this polarized light can be resolved into two com-
ponents, km and kl, on the right figure, of which only kl can pass
through the second crystal.
In Figure 4.4, light transmitted from below is polarized parallel to PP,
so when the analyser is oriented at right angles to the polarizer, no light is
transmitted through the analyser because it can only transmit light polarized
parallel to AA. When the crystals are inclined, the vibrations parallel to P'P'
can be resolved into two directions normal to each other. The amplitude
parallel to the axis of the polarizer can be considered proportional to kn,
and this can be resolved into two components, km and kl (each propor-
tional to its length). Of these two, only kl is transmitted by the analyser, km
being absorbed. As the polarizer is rotated, the kl component changes its
amplitude, becoming zero when the crystals are crossed at 90". The colour
is not changed, but the brightness is. The brightness of the transmitted light
is proportional to the cosine of the angle between the polarizer and the
analyser.
When the polars of a microscope are crossed, no light is transmitted
through it. When any isotropic substance, such as glass, is placed on the
microscope stage (between the polarizer and the analyser) it remains dark.
If a crystal that is placed on the microscope stage also remains dark, that
crystal belongs to the cubic system. A crystal of any other system, however,
will allow some light to be transmitted because the birefringence (see section
Birefringence) re-orientates the plane of polarization and some light can then
pass through the analyser.
Crystals affect the passage of light in some interesting and important ways.
A ray of light entering a crystal of the cubic system is refracted just as it
would be by glass and the refracted ray is in the plane of incidence; but all
the other systems give rise to two refracted rays, at least one of which does
not necessarily lie in the plane of incidence.
The nicol prism is a device for polarizing and analysing the directions of
vibration of light. It consists of a crystal of calcite (CaC03) in a pure form
Copyright 2002 by Richard E. Chapman