Physics for Geologists, Second edition

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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 principal 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 components, 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 proportional 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
50 Optics called Iceland Spar. Two slices of Iceland Spar, cut normal to the optic axis, are cemented with Canada balsam. The incident light on the prism gives rise to two refracted rays, one of which is totally reflected by the balsam, the other transmitted. The transmitted ray is polarized. In a petrological microscope, one nicol prism is used to polarize the light (the polarizer), another is used to analyse it (the analyser). In modern petrological microscopes, the nicol prism has been replaced by polars that are made of polaroidTM, but the effect is the same. Optical activity Some substances have the ability to rotate the plane of polarization of light passing through them. This is called optical activity. These substances, usu- ally natural organic substances, have asymmetric molecules. Crude oil is such a substance, and it is a strong argument for the organic origin of petroleum. Pleochroism, dichroism and trichroism Minerals in thin section that change colour, either hue or intensity, when rotated on a stage in polarized light are called pleochroic and the process is called pleochroism. Minerals with only one optic axis (those belonging to the hexagonal and tetragonal systems) show two characteristic colours. Those with two optic axes - the biaxial minerals, which belong to the orthorhom- bic, monoclinic and anorthic systems - show three characteristic colours. Isotropic minerals are not pleochroic because the absorption of light is equal in all directions. Changes of colour or hue are due to unequal absorption of light of different frequencies (or wavelengths) in different orientations; and changes in intensity are due to loss of amplitude in different orientations. Tourmaline (hexagonal, trigonal) is a uniaxial mineral, and we have seen that no polarized light is transmitted through crystals cut parallel to the optic axis when its axis is at 90° to the direction of polarization. In other orientations light is partly absorbed. Basal sections of uniaxial minerals do not show pleochroism because absorption of light of all wavelengths is equal in all directions. Pleochroic haloes, due to small inclusions of a radioactive contaminant, are common in tourmaline. Biotite (monoclinic, pseudo-hexagonal; biaxial) is a common pleochroic mineral. In sections other than basal, its colour changes from a dark brown, when the cleavage is parallel to the plane of polarization, to yellow. Specialists may use the term dichroism for uniaxial minerals, because these show two characteristic colours. Similarly, trichroism may be used for biaxial minerals, which show three characteristic colours. Birefringence Anisotropic crystals are found to have one index of refraction for light linearly polarized in one direction, and another for light linearly polarized in Copyright 2002 by Richard E. Chapman
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
Page 15 and 16: xviii Acknowledgements to K. Whaler
Page 17 and 18: xx Symbols mass refractive index bu
Page 19 and 20: 2 Basic concepts Table 1.1 Dimensio
Page 21 and 22: 4 Basic concepts Table 1.2 Basic SI
Page 23 and 24: 6 Basic concepts pascal (Pa) and si
Page 25 and 26: 8 Basic concepts all the relevant d
Page 27 and 28: 10 Basic concepts relating them by
Page 29 and 30: 2 Force The dimensions of force are
Page 31 and 32: 14 Force The ratio of the Moon's ac
Page 33 and 34: 16 Force Figure 2.1 The sum of the
Page 35 and 36: 18 Force When a motorcycle takes a
Page 37 and 38: 20 Force Figure 2.3 Torque is the p
Page 39 and 40: 22 Force How does momentum differ f
Page 41 and 42: 24 Force the weights - that is, the
Page 43 and 44: 26 Force Figure 2.6 Wall-sticking i
Page 45 and 46: 3 Gravity Universal gravity When di
Page 47 and 48: 30 Gravity are significant to geolo
Page 49 and 50: 32 Gravity Figure 3.2 The tractive,
Page 51 and 52: 34 Gravity Mean sea level It might
Page 53 and 54: 36 Gravity The benefits of space fl
Page 55 and 56: 38 Gravity Figure 3.6 Profile of th
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65: 48 Optics only the light oscillatin
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
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10 Sea waves The nature of water wa
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Sea waves 103 Figure 10.1 Wave moti
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Sea waves 105 refraction by islands
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Acoustics: sound and other waves 10
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Acoustics: sound and other waves 10
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12 Fluids and fluid flow Introducti
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Fluids and fluid flow 1 13 Figure 1
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Fluids and fluid flow 115 Figure 22
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Fluids and fluid flow 117 and the f
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water above a vertical thickness h
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Fluids and fluid flow 121 where V i
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Fluids and fluid flow 123 ardentes,
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Fluids and fluid flow 125 Figure 12
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- 14 $ 12 E 10 K .- 3 8 r cll + 6 0
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Fluids and fluid flow 129 the liqui
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Some dangers of mathematical statis
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Appendix 139 What would happen if y
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Notes 141 and since x is very large
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References Allum, J. A. E. (1966) P
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References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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