Optical Mineralogy PG 201: Understanding the Properties of Minerals through Light, Lecture notes of Geology

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Optical Mineralogy

PG 201

By: Dr. Hossam Helba

Optical Mineralogy PG 201 Dr. Hossam Helba 1

Optical mineralogy is concerned with studying the optical properties of minerals

that depend on the manner by which visible light is transmitted through thin

sections of transparent or translucent minerals by using polarizing microscope.

What is Optical Mineralogy and why do we study it?

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Optical Mineralogy PG 201 Dr. Hossam Helba

References

Nesse, W. D., 2004. Introduction to optical mineralogy. Oxford University Press, 348 pp.

Kerr, P.F., 1977. Optical mineralogy (4th^ Edition). New York (McGraw Hill Book Company), 492 PP.

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Optical Mineralogy PG 201 Dr. Hossam Helba

• Light is a form of energy that can be detected with the eye, and is transmitted from one place to another at finite velocity.
• Visible light is a small portion of the electromagnetic spectrum , which ranges from cosmic rays to radio waves. It has wavelengths of between about 400 and 700 nm in a vacuum.

Lecture 1

Nature and Properties of Light

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Optical Mineralogy PG 201 Dr. Hossam Helba

Nature of light

Theories developed to determine the nature of light: 1- Wave theory by Higgins 2- Corpuscular theory by Newton 3- Electromagnetic wave theory by Maxwell 4- Quantum theory by Planck

Both the particle and wave theories have been shown to be correct and can be considered as complementary theories. But, because wave theory describes effectively the phenomena of polarization, reflection, refraction, and interference-the meet of an optical mineralogy course- so we treat light as electromagnetic radiation.

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Optical Mineralogy PG 201 Dr. Hossam Helba

Wave motion of light

It is a simple harmonic movement combined with regular forward motion.

Simple harmonic motion is regular movement in a circular path looks as if

it were projected on the diameter of the circle

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Optical Mineralogy PG 201 Dr. Hossam Helba

Refractive index, n , of a material or substance is defined as the ratio of the speed of light in a vacuum, VC , to the speed of light in a material through which it passes, Vm

n = VC / Vm

• Note that the value of refractive index will always be greater than 1.0, since Vm can never be greater than VC. In general, Vm depends on the density of the material, with Vm decreasing with increasing density. Thus, higher density materials will have higher refractive indices.
• The refractive index of any material depends on the wavelength of light because different wavelengths are interfered with to different extents by the atoms that make up the material. In general refractive index varies linearly with wavelength.

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Optical Mineralogy PG 201 Dr. Hossam Helba

Isotropic and anisotropic materials

• Isotropic material is a material in which the velocity of light is the same in all directions. They include gases, liquids, amorphous materials (as glasses) and minerals in the cubic system.
• Anisotropic material is a material in which light travels at a different speed in different directions. They include minerals in tetragonal, hexagonal, trigonal, orthorhombic, monoclinic and triclinic systems.
• Any isotropic material has a single constant refractive index for each wavelength.
• Any anisotropic material is characterized by the phenomenon of double refraction, where any ray passes through it splits into two rays vibrating perpendicular to each other. Anisotropic materials will have a range of refractive indices between two extreme values for each wavelength.

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Optical Mineralogy PG 201 Dr. Hossam Helba

For Refraction

• Angle of incidence ≠ angle of refraction
• The angle of refraction is dependent on the angle of incidence and the refractive index ,n of the materials on either side of the interface according to Snell’s law : ni sin (i) = nr sin (r)
• A high refractive index indicates low velocity and vice versa

Snell’s law

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Optical Mineralogy PG 201 Dr. Hossam Helba

When light passes from a high index material to a low index material, the angle of refraction will be larger than the angle of incidence.

Light with an angle of incidence greater than the critical angle (CA) cannot be refracted into the low-index material.

The critical angle is the angle of incidence that yields an angle of refraction of 90º

Critical Angle and Total Internal Reflection

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Optical Mineralogy PG 201 Dr. Hossam Helba

The light passing through a mineral or through space commonly passes as a beam of light rather than a single wave. In this case a wave front is a surface that connects similar points on adjacent waves or connects points of the same phase. A line constructed at right angles to the wave front is called the wave normal and represents the direction that the wave is moving. In isotropic materials (light velocity the same in all directions), the light ray and wave normal coincide_._ In anisotropic materials (light velocity different in different directions) the wave normal and light ray directions usually are not parallel.

Wave front and wave normal

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Optical Mineralogy PG 201 Dr. Hossam Helba

Interference of light waves

If two waves travel along the same path, they can interfere with each other. The distance that one wave lags behind the other is called the retardation (Δ). It can be described either in terms of the distance in nanometers, or in terms of the number of wavelengths that one wave lags the other. If the two waves vibrate in the same plane three cases of interference occur: 1- When the retardation equals an integral number of wavelengths Δ = i λ the two waves are in phase. They constructively interfere with each other to produce a resultant wave that is the arithmetic sum of the two. 2- When the retardation equals ½ , 1 ½, 2 ½, etc. wavelengths, the two waves are out of phase. They destructively interfere and cancel each other. 3- When the retardation is some intermediate value, the light is partially in phase (or partially out of phase, if you prefer) and the interference is partially constructive (or partially destructive).

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Optical Mineralogy PG 201 Dr. Hossam Helba

Polarization of light

Normal light vibrates equally in all direction perpendicular to its path of propagation. If the light is constrained to vibrate in only one plane, however, we say that it is plane polarized light.

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Optical Mineralogy PG 201 Dr. Hossam Helba

Unpolarized and Polarized Light

 Unpolarized light

 Vibrates in all directions perpendicular to direction of propagation  Occurs only in isotropic materials like isometric crystals, Air, water, glass, etc.

 Polarized light

 Vibrates in only one direction

 Plane, circular, and elliptical polarization were recognized- we focus on plane polarized light

 Plane polarized light can be achieved by:

(1) Refraction

(2) Reflection

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Optical Mineralogy PG 201 Dr. Hossam Helba