The Properties of Light

Before we learn about the properties of light, let's watch this video......

The optical properties of crystals are, next to x-ray diffraction and direct chemical analyses, the most reliable properties available to distinguish and identify minerals.
The optical properties depend on the manner that visible light is transmitted through the crystal, and thus are dependent on crystal structure, crystal symmetry, and chemical composition of the mineral.

In order to understand the optical properties of crystals we must first understand something about light and how it interacts with matter.

 Light

 Light is electromagnetic radiation that has properties of waves.  The electromagnetic spectrum can be divided into several bands based on the wavelength of the light waves.  As we have discussed before, visible light represents a narrow group of wavelengths between about 380 nm (1 nm = 10^-9 m) and 730 nm.

 Our eyes interpret these wavelengths as different colors.  If only a single wavelength or limited range of wavelengths are present and enter our eyes, they are interpreted as a certain color.  If a single wavelength is present we say that we have monochromatic light.  If all wavelengths of visible light are present, our eyes interpret this as white light.  If no wavelengths in the visible range are present, we interpret this as dark. 

Interaction of Light with Matter

 Velocity of Light and Refractive Index
The energy of light is related to its frequency and velocity as follows:

E = hn = hC/l

where E = energy
h = Planck's constant, 6.62517 x 10^-27 erg^.sec
n = frequency
C = velocity of light = 2.99793 x 10¹⁰  cm/sec
l = wavelength

The velocity of light, C, in a vacuum is 2.99793 x 10¹⁰cm/sec.  Light cannot travel faster than this, but if it travels through a substance,  its velocity will decrease.  Note that from the equation given above- 

C = nl

The frequency of vibration, n, remains constant when the light passes through a substance.  Thus, if the velocity, C, is reduced on passage through a substance, the wavelength, l, must also decrease.

We here define refractive index, n, of a material or substance as the ratio of the speed of light in a vacuum, C,  to the speed of light in a material through which it passes, C_m.

n = C/C_m

Note that the value of refractive index will always be greater than 1.0, since C_m can never be greater than C.  In general,  C_m depends on the density of the material, with  C_m 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. 

Materials can be divided into 2 classes based on how the velocity of light of a particular wavelength varies in the material.

1. Materials whose refractive index not depend on the direction that the light travels are called irotropic materials.  In these materials the velocity of light does not depend on the direction that the light travels.  Isotropic materials have a single, constant refractive index for each wavelength.  Minerals that crystallize in the isometric system, by virtue of their symmetry, are isotropic.  Similarly, glass, gases, most liquids and amorphous solids are isotropic.
2. Materials whose refractive index does depend on the direction that the light travels are called anisotropic materials.  These types of materials will have a range of refractive indices between two extreme values for each wavelength.  Anisotropic materials can be further divided into two subclasses, although the reasoning behind these subdivisions will become clear in a later lecture.

•  Minerals that crystallize in the tetragonal and hexagonal crystal systems (as well as some plastics) are uniaxial and are characterized by 2 extreme refractive indices for each wavelength.
• Minerals that crystallize in the triclinic, monoclinic, and orthorhombic crystal systems are biaxial and are characterized by 3 refractive indices, one of which is intermediate between the other two.

 Air, since it is a gas, is isotropic.  The refractive index of air is usually taken as 1.0, although its true value is 1.0003.

Reflection and Refraction of Light

When light strikes an interface between two substances with different refractive indices, two things occur. An incident ray of light striking the interface at an angle, i, measured between a line perpendicular to the interface and the propagation direction of the incident ray, will be reflected off the interface at the same angle, i.  In other words the angle of reflection is equal to the angle of incidence. 

If the second substance is transparent to light, then a ray of light will enter the substance with different refractive index, and will be refracted, or bent, at an angle r, the angle of refraction.  The angle of refraction is dependent on the angle of incidence and the refractive index of the materials on either side of the interface according to Snell's Law: 

n_i sin (i) =  n_r sin (r)

Note that if the angle of incidence is 0^o (i.e. the light enters perpendicular to the interface) that some of the light will be reflected directly back, and the refracted ray will continue along the same path.  This can be seen from Snell's law, since sin(0^o) = 0, making sin (r) = 0, and resulting in r = 0.

There is also an angle, i_c, called the critical angle for total internal reflection where the refracted ray travels along the interface between the two substances.

 

This occurs when the angle r = 90^o.  In this case, applying Snell's law: 

n_i sin (i_c) = n_r sin (90^o) = n_r   [since sin (90^o) = 1]

sin (i_c) = n_r/n_i

 

Dispersion of Light

The fact that refractive indices differ for each wavelength of light produces an effect called dispersion.  This can be seen by shining a beam of white light into a triangular prism made of glass. White light entering such a prism will be refracted in the prism by different angles depending on the wavelength of the light. 

The refractive index for longer wavelengths (red) are lower than those for shorter wavelengths (violet).  This results in the a greater angle of refraction for the longer wavelengths than for the shorter wavelengths.  (Shown here are the paths taken for a wavelength of 800 nm, angle r₈₀₀ and for a wavelength of 300 nm, angle r₃₀₀ ). When the light exits from the other side of the prism, we see the different wavelengths dispersed to show the different colors of the spectrum.

  Absorption of Light

 When light enters a transparent material some of its energy is dissipated as heat energy, and it thus looses some of its intensity.  When this absorption of energy occurs selectively for different wavelengths of light, they light that gets transmitted through the material will show only those wavelengths of light that are not absorbed.  The transmitted wavelengths will then be seen as color, called the absorption color of the material.

For example, if we measure the intensity of light, I_o,  for each wavelength before it is transmitted through a material, and measure the intensity, I, for each wavelength after it has passed through the material, and plot I/I_o versus wavelength we obtain the absorption curve for that material as shown here.   The absorption curve (continuous line) for the material in this example shows that the light exiting the material will have a yellow-green color, called the absorption color.  An opaque substance would have an absorption curve such as that labeled "Dark", i.e. no wavelengths would be transmitted.  Sunlight, on passing through the atmosphere has absorption curve as shown, thus we see it as white light, since all wavelengths are present.

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 on plane, however, we say that it is plane polarized light. The direction that the light vibrates is called the vibration direction, which for now will be perpendicular to the direction.  There are two common ways that light can become polarized.

• The first involves reflection off of a non-metallic surface, such as glass or paint.  An unpolarized beam of light, vibrating in all directions perpendicular to its path strikes such a surface and is reflected.  The reflected beam will be polarized with vibration directions parallel to the reflecting surface (perpendicular to the page as indicated by the open circles on the ray path).  If some of this light also enters the material and is refracted at an angle 90^o to the path of the reflected ray, it too will become partially polarized, with vibration directions again perpendicular to the path of the refracted ray, but in the plane perpendicular to the direction of vibration in the reflected ray (the plane of the paper, as shown in the drawing).
• Polarization can also be achieved by passing the light through a substance that absorbs light vibrating in all directions except one.  Anisotropic crystals have this property in certain directions, called privileged directions, and we will discuss these properties when we discuss uniaxial and biaxial crystals.  Crystals were used to produce polarized light in microscopes built before about 1950. The device used to make polarized light in modern microscopes is a Polaroid, a trade name for a plastic film made by the Polaroid Corporation.  A Polaroid consists of long-chain organic molecules that are aligned in one direction an placed in a plastic sheet.  They are placed close enough to form a closely spaced linear grid, that allows the passage of light vibrating only in the same direction as the grid.  Light vibrating in all other directions is absorbed.  Such a device is also called a polarizer. 

If a beam on non-polarized light encounters a polarizer, only light vibrating parallel to the polarizing direction of the polarizer will be allowed to pass.  The light coming out on the other side will then be plane polarized, and will be vibrating parallel to the polarizing direction of the polarizer.  If another polarizer with its polarization direction oriented perpendicular to the first polarizer is placed in front of the beam of now polarized light, then no light will penetrate the second polarizer.  In this case we say that the light has been extinguished.

Polaroid sunglasses use these same principles.  For example, incoming solar radiation is reflected off of the surface of the ocean or the painted hood of your car.  Reflected light coming off of either of these surfaces will be polarized such that the vibration directions are parallel to the reflected surface, or approximately horizontal (as in the first method of polarization discussed above).  Polaroid sunglasses contain polarizers with the polarization direction oriented vertically.  Wearing such glasses will cut out all of the horizontally polarized light reflecting off the water surface or hood of your car.

source : http://www.tulane.edu/~sanelson/geol211/proplight.htm
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