Page 192 - A Practical Introduction to Optical Mineralogy

ISOTROPY
Light of the same wavelength and the same or different intensity may
4 Transmitted-light be in phase as illustrated in Figure 4.lb, or out of phase as shown in
Figure 4.lc. The path difference may be measured as a fraction of the
crystallography wavelength.
If two coherent rays (originating at the same instant from the same
source) which are exactly in phase are combined, they are added
together and intensity is enhanced. If the rays are slightly out of phase,
the enhancement is reduced. If the rays have the same amplitude and
4.1 Polarised light: an introduction
have a path difference of half a wavelength, the vibration will be cancel-
led and amplitude will be zero.
Light is an electromagnetic vibration but, for the purpose of
In transmitted-light microscopy, linearly polarised white light travels
transmitted- (and reflected) light microscopy, light can be considered as up the microscope axis, which is normal to the plane of the thin s~ction.
being simply the transfer of energy by vibrating 'particles' along a path
On entering an anisotropic (see Section 4.3) crystalline substance
from the source to the observer. White light consists of many rays,
rotated from the extinction position, the light can be considered to be
ranging in wavelength from 380 to 770 nm through the visible spectrum.
separated into two components which travel with different velocities
However, it is simpler to consider the idealised case of a single ray of
through the crystal. On leaving the crystal the two components may be
monochromatic light, that is light of a single wavelength (Fig. 4.la). The
out of phase and the path difference will vary for different wavelengths
wave is generated by vibration of particles (e.g. A) lying along the path
of light. This complexity in the light leaving the crystal is only apparent
of the ray. If the light is non-polarised, the particles vibrate at random in
when the analyser is inserted and interference colours are generated
a plane normal to the direction of the ray. If the light is linearly (or plane)
(see Section 4.6).
polarised by means of a polarising filter, then the particles simply vibrate
up and down along the line xy.
4.2 Refractive index
The refractive index of a medium (RI or n) is defined as the ratio of the
~~v v with wavelength but the variation is usually small for transparent min-
velocity of light in the medium to that in vacuo. Refractive index varies
erals, so single ' white light' refractive indices are usually used.
A
If V, and V 2 are the velocities of light in two different media, and i is
X
the angle of incidence of the light in one medium and r is its angle of
refraction in the other, then (see Fig. 4.2):
~ be b'c sin i sin i refractive index
(b) v2 b'c' b'c sin r sin r
The refractive index of a medium is inversely proportional to the vel-
ocity of light (for a specific wavelength) through the medium, i.e.
RIa: 1/V.
(c) 4.3 Isotropy

Isotropic crystals transmit light with equal velocity in all directions. A
ray velocity surface represents the surface composed of all points
Figure 4.1 (a) Monochromatic light. (b) Two waves of the same wavelength, reached by light travelling along all possible rays from a point source
but different intensity, in phase. (c) Two waves of the same wavelength, but within a crystal in a given time. In isotropic crystals, the ray velocity
different intensity, out of phase. surface is a sphere.
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