Physics for Geologists, Second edition

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Optics 45 know whether the light was at B or B1. The principle of reciprocity requires that light travelling in the reverse directions traverses the same paths. (Do not forget that light is going out from the point in all directions, but we only see that which arrives first.) In Figure 4.3, the light travels from a plane source AA1. When the ray from A reaches the interface at B, the remainder of the plane wave front BC still has some distance to travel in air while the ray at B continues in the other medium. The frequency of the plane wave remains the same, but its speed changes, so its wavelength also changes. In the time taken for the incident ray to travel from B' to C', the refracted ray travels a shorter distance (in this case) from B to C, and the direction of the wave front is altered. The refracted wave is parallel to CC1. When the incident light is in the medium with larger refractive index, smaller speed ci < c, (Figure 4.2(b)), the angle of refraction is larger than the angle of incidence. As the angle of incidence increases, so the angle of refraction increases until the refracted ray is in the plane of contact between the two media and the angle of refraction is 90". This angle of incidence is called the critical angle, i,, and at any angle of incidence greater than i, the ray is totally reflected. You can see this when diving. Looking upwards, you can see things above the surface; but there is an angle i, from the vertical greater than which the surface appears as a mirror - which indeed it is. Snell's law tells us that i, = sin-' ci/c, where ci is the speed of light in the denser medium and c, that in air. This is the inverse of the relationship that gives the refractive index, so i, = sin-' (lln). For water with a refractive index of 1.333, the critical angle is about 48.6". For very precise work we would have to take into account that the speed of light, c, is not quite the same in air as in a vacuum (the refractive index of air is 1.0002). Snell's Law applies to the reflection and refraction of sound and seismic waves as well (see page 107). Copyright 2002 by Richard E. Chapman Figure 4.3 Huygen's geometric construction of the refraction path, in section. When the wave-front AA' reaches BB', it begins to be refracted. The velocity in the lower medium is less than that in the above, so the wave only travels the distance BC in the time it takes the wave at B' to reach C'.
46 Optics The coeficient of reflection is the ratio of the intensity, I, of the normal incident to the normal reflected light (the basic SI unit of luminous intensity is the candela, cd): In geology, we are also concerned with the reflectance of coal-like material, particularly vitrinite, in studies of coals and the diagenesis of sedimentary rocks. Reflectance, R or p, is the ratio of reflected radiant flux, which is the time rate of reflected radiant energy (W = J s-l), to the incident radiant flux: Refractive index As mentioned above, the refractive index is the ratio of the incident wave speed to the refracted wave speed for light passing from a vacuum into a denser medium. It is also the ratio of the sine of the angle of incidence and the sine of the angle of refraction: ci sin i n=-=-. cr sin r However, the amount of refraction, and so the refractive index, also depends upon the wavelength of the light, the refractive index increasing as wavelength decreases. The variation of refractive index with wavelength is called dispersion, and chromatic aberration in the context of lenses because different colours focus on slightly different planes (many camera lenses have a mark for infrared focus at co, which is less than the scale for normal light at co). White light, being a mixture of colours and therefore of frequencies and wavelengths, is split into a spectrum of colours by its passage through a prism. The light is refracted on entry into the prism, and again on exit, with violet refracted most, then indigo, blue, green, yellow, orange, to red. With yellow light with a wavelength of 589 nm, typical refractive indices are: air, 1.0002; water, 1.333; glass, about 1.5; Canada balsam, 1.54; diamond, 2.417. It is its very high refractive index that gives the cut diamond its sparkle. Calcite and quartz are examples of minerals that have two refractive indices, depending on the orientation of the crystal. This is called birefringence and it will be discussed when we have considered polarization of light. Interference Interference is produced when two light sources are superimposed. If two wave trains of the same wavelength and in the same phase, but of different 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.
Page 11 and 12: xiv Preface waves diminishes with d
Page 13 and 14: 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: 44 Optics Figure 4.2 Refraction. (a
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
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
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Fracture Stress and strain 97 We fo
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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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