Page 200 - A Practical Introduction to Optical Mineralogy

TRANSMITTED-LIGHT CRYSTALLOGRAPHY INTERFERENCE COLOURS AND NEWTON'S SCALE
Figure 4.13
Destructive A components OD and OD' are still equal and coincident and a wave of
inferference.
X In the oo position XX' and YY' are coincident with PP' and AA'
p~~--~~~~~~p·
X'
A'
whatever the angular position of the crystal section, and the result is a
wave of zero amplitude (destructive interference). In Figure 4.13, PP' is
the polariser transmission plane, AA' is the analyser transmission plane,
XX' and YY' are the two components into which light is resolved on
passing through the crystal, OBis the amplitude of the wave leaving the
polariser, OC and OC' are the amplitudes of the two components after
passing through the crystal plate, and OD and OD' are the amplitudes of
these components resolved in the analyser transmission plane. When the
crystal is in the 4SO position in Figure 4.13, OD and OD' are equal and
opposite and yield a resultant wave of zero amplitude. In the 15°
position, although components OC and OC' are dissimilar, OD and
OD' are equal and opposite and a wave of zero amplitude again results.
If m is an odd number, then the components transmitted by the
analyser are in phase and superimposed, so that a maximum resultant
wave is produced with the crystal in the 45° position which has twice the
amplitude of either of the interfering waves. The intensity of light of this
resultant wave is four times as great as the intensity of the light of either
wave because intensity is proportional to square of amplitude. This case
is illustrated in Figure 4.14. In this figure the notation is as before. This
time, however, the components reinforce in the analyser transmission
plane. In the 45° position in Figure 4.14, OD' and OD are equal and
coincident, and therefore analyser transmitted amplitude is 20D. In the
A
p P' p
X'
Figure 4.14
Constructive
interference. A' A' Y'
188
15° position, although components OC and OC' are dissimilar, the
amplitude 20D again results. In Figure 4.14, the analyser transmitted
amplitude is OG = OD + OD' .
respectively. The components have no value (since D and D' would be
coincident with 0) and therefore extinction would result. Thus from the
above discussion resultant waves have a maximum amplitude (and
maximum light intensity) in the 45° position, a smaller amplitude in the
15° position and zero amplitude in the parallel position; in this way a
mineral will extinguish four times during a complete (360°) rotation of
the microscope stage. Any path difference produced by a crystal frag-
ment results in illumination, but the intensity decreases as the path
difference approaches the wavelength.
The origin of interference colours can best be understood by consid-
ering the quartz wedge, remembering that varying the thickness of a
crystal plate produces a variation in the path difference (or retardation).
If a wedge cut parallel to the c axis of a crystal of quartz (<ln = 0.009) is
inserted into the path of monochromatic sodium light passing through a
microscope, then bright yellow bands are seen where the thickness of the
wedge results in a path difference of m'A/2 with m an odd number, and
dark bands are seen where m is an even number. The wavelength of
sodium light is 580 nm, and therefore the bright yellow bands occur
when <lnt = 580 x 1/2, 580 x 3/2, 580 x 5/2 nm etc., and the dark bands
occur when <lnt = 580, 580 x 2, 580 x 3 nm etc.
White light is composed of wavelengths ranging from 380 nm to
770 nm (violet to red). A quartz wedge inserted into the path of white
light through a microscope produces a 'spectrum' of colours. Each
different wavelength gives darkness and maximum intensity of colour
for that wavelength at different positions along the wedge (Fig. 4.15).
Overlapping of these various darknesses and maximum intensities com-
bines to form a series of colours, known as Newton's Scale, which is
shown in the colour chart (back cover). The colours are divided into
different orders. The colours of the first order are black, grey, white,
yellow and finally red. In the second order the colours are violet, blue,
green, yellow, orange and red. Above this the colours become fainter,
and the third order consists of indigo, green/blue, yellow, red and violet.
Above the third order, mixing of wavelengths produces an easily
identifiable pink colour.
In summary, the interference colour produced by an anisotropic
mineral grain in a thin section depends on the retardation effect, which
depends on the birefringence of the grain and its thickness.
189