guide to thin section microscopy - Mineralogical Society of America

Guide to Thin Section Microscopy
Double refraction
Retardation refers to the accumulated distance between the wave front of the fast wave
(correlating with n x ') and that of the slow wave (correlating with n z ') by the time the slow
wave reaches the crystal surface. As both waves revert back to identical wave velocity after
leaving the crystal, retardation remains constant in the microscope from that point onwards,
unless these light waves pass through another crystal (which they do if an accessory plate is
inserted; see Ch. 4.2.4). In thin section microscopy, retardation is expressed in nm. In
macroscopic crystals, retardation can be in the order of millimetres. Taking calcite as an
example, O-wave and E-wave passing through a cleavage rhombohedron of 2 cm thickness
have accumulated a retardation of 1.84 mm as they exit the crystal (light path orthogonal to
rhomb faces).
The amount of retardation is determined by two factors, (1) the difference between the two
wave velocities, or expressed differently, by the birefringence value (∆n = n z ' – n x ') of the
particular crystal section observed; and (2) by the thickness (d) of the crystal plate in the thin
section. Thus, Γ = d * (n z ' – n x ').
The distance between bottom and top of the crystal plate (i.e., thickness d) can also be
expressed as multiples of wavelengths (d = m*λ). As light of an initial wavelength λ i enters
the crystal, two waves with different wavelengths are generated (slow wave: λ z' = λ i /n z' ; fast
wave: λ x' = λ i /n x' ). If d is expressed as multiples of λ z' and λ x' , we get
d = m 1 *λ z' = m 2 *λ x' or m 1 = d/λ z' and m 2 = d/λ x'
Retardation is the difference between the multipliers m 1 and m 2 , multiplied by wavelength λ i :
Γ = (m 1 – m 2 ) * λ i .
Note that by the time the slow wave reaches the upper crystal surface, the fast wave has
reverted to λ i and travelled the distance Γ outside the crystal.
Thus, Γ = (d/λ z' – d/λ x' ) * λ i
as λ z' = λ i /n z' and λ x' = λ i /n x' ,
Γ = (d * n z' /λ i – d * n x' /λ i )∗λ i = d * (n z' - n x' ).
Raith, Raase & Reinhardt – February 2012
After leaving the crystal, the two waves with amplitudes a 1 and a 2 enter the analyzer with the
retardation obtained within the crystal plate. As shown by vector decomposition (Fig. 4-24)
two waves of the same wavelength but reduced amplitudes (a 1 ' and a 2 ') come to lie in the
analyzer's plane of polarization. The orthogonally oriented wave components are blocked by
the analyzer. The relative amplitudes a 1 ' and a 2 ' of the transmitted waves depend entirely on
the orientation of the vibration directions with respect to the polarizer and analyzer directions.
They have their minimum (zero) in the dark image (= extinction) position and reach their
maximum after rotation of 45° from the extinction position, in the diagonal position (Figs. 4-
23, 4-24).
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