guide to thin section microscopy - Mineralogical Society of America

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Guide to Thin Section Microscopy Double refraction there is no discernible change in light intensity as the stage is rotated (at least in colourless minerals), simply because the total light intensity from a 1 and a 2 remains constant. Anisotropic coloured minerals are, of course, expected to show a variation of absorption as the stage is turned (Ch. 4.2.1), and high-birefringent minerals may show variable refraction effects (Fig. 4-22). As both waves propagate in the crystal with different velocities (and correspondingly different refractive indices n z ' and n x '), a specific phase shift (= retardation gamma) is created by the time the light reaches the upper crystal surface (Fig. 4-24; in this example, the phase shift Γ is λ/2). Raith, Raase & Reinhardt – February 2012 Figure 4-24. Vector construction for light intensities as the mineral is rotated from the extinction position into a 45˚ diagonal position. 83
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). 84
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