Optical Mineralogy

Nature of Light
 Optical Mineralogy
• Optical mineralogy - the study of the interaction of light with minerals, most
commonly limited to visible light and usually further limited to the non-
opaque minerals.

• The optical properties of minerals are related to the crystal chemistry of the
mineral. So, a simple optical measurement with a polarizing microscope can
yield important information about some crystal structure-chemical
composition aspect of the mineral under study.

• The most general application of optical mineralogy is to aid in the

identification of minerals, either in rock thin sections or individual mineral
grains
 Light
Light can be thought of both as a ….
• Wave phenomenon (electromagnetic theory): The wave
theory of light describes light as a transerse wave, with the
direction of propagation and the direction of energy transfer
being perpendicular
• Particle phenomenon (quantum theory): The particle
theory describes light as composed of photons of different
energies with these energies related to the wavelength in the
electromagnetic theory
 Light as wave
Light is electromagnetic radiation that has properties of waves. The electromagnetic
spectrum can be divided into several bands based on the wavelength

If a single wavelength is present we say that we have monochromatic light.

Interaction of Light with Matter
Reflection of light:
The law of reflection states that when a ray
of light reflects off a surface, the angle of
incidence is equal to the angle of reflection.

Refraction of light:
Refraction is the bending of the path of a
light wave as it passes across the boundary
separating two media. Refraction is caused
by the change in speed experienced by the
light wave when it changes medium.

Light can either refract towards the normal

(when slowing down while crossing the
boundary) or away from the normal (when
speeding up while crossing the boundary).
 Refractive Index
• Refractive index is the measure of the bending of a ray of light when
passing from one medium into another.
If i is the angle of incidence of a ray in vacuum (angle between the
incoming ray and the perpendicular to the surface of a medium, called the
normal) and r is the angle of refraction (angle between the ray in the
medium and the normal), the refractive index n is defined as the ratio of
the sine of the angle of incidence to the sine of the angle of refraction;

i.e., n = sin i / sin r.

• Refractive index of a mineral is equal to the velocity of light of a
given wavelength in vacuum divided by its velocity v in the mineral.

Refractive index, n C C = v/ m

where, n = refractive index of mineral, Cv = velocity of light in a vacuum, Cv =

velocity of light in the mineral
 Snell’s Law
• Willebrod Snellius (1591-1626), professor of mathematics at Leyden in Holland, in
about 1621, formulated the Law of Refraction, also known as the Snell’s Law, describing
the relationship between the paths of the incident and refracted rays.

• The relationship between the angles of incidence and refraction and the indices of
refraction of the two media is known as Snell's Law. Snell's law applies to the refraction
of light in any situation, regardless of what the two media are.

ni sin (i) = nr sin (r)

Where i=angle of incidence
R= angle of refraction
n= refractive index of material
 Total Internal Reflection

Total internal reflection (TIR) is the phenomenon that involves the reflection of all the
incident light off the boundary. TIR only takes place when both of the following two
conditions are met:
1. the light is in the more dense medium and approaching the less dense medium.
2. the angle of incidence is greater than the so-called critical angle.
 Critical Angle

Total internal reflection occurs because the angle of refraction reaches a 90-degree angle before
the angle of incidence reaches a 90-degree angle. The only way for the angle of refraction to be
greater than the angle of incidence is for light to bend away from the normal. TIR only occurs
with large angles of incidence, if the angle of incidence is greater than the critical angle for the
particular combination of materials.

The critical angle is defined as the angle of incidence that provides an angle of refraction of 90-
degrees. Make particular note that the critical angle is an angle of incidence value.
(1) The refractive index of a vacuum is 1.0.
(2) Refractive index is a unitless number.
(3) Because the velocity of light cannot exceed that in a vacuum (3x108 m/s),
the refractive index of any material is greater than 1.

Generally, any mechanism that increases electron density in a material also

increases refractive index.
So, increasing the density of a material usually increases the refractive index.
However, refractive index is also closely related to bonding. In general, ionic
compounds having lower values of n than covalent ones
 Velocity of light, its wavelength
The energy of light is related to its frequency and velocity as follows:
E = hν = hC/λ
i.e. C = νλ
where E = energy
h = Planck's constant, 6.62517 x 10-27 erg.sec
ν = frequency
C = velocity of light = 2.99793 x 1010 cm/sec
λ = 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.

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

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.
 Dispersion of light
The refractive index of a material depends upon the wavelength of light
and can be written mathematically:
n = f (l )
where,
n = refractive index of mineral
l = wavelength of light
This change in refractive index is called dispersion

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.
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, then 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.
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.

Different ways light can be

polarized:
(i) Reflection (and refraction) off of a
non-metallic surface
(ii) passing the light through a
substance that absorbs light
vibrating in all directions except one
 Plane polarized light

Plane polarized light, showing wavelength, ray path, moving in the x direction, and
vibration direction perpendicular to X in the Y direction. The light is plane polarized
in the XY plane. The vibration direction is perpendicular to the ray path in isotropic
and certain directions in anisotropic crystals.
 How to obtain PPL

Reflection on a smooth surface

Absorption by a polaroid
Refraction, as in a
Refraction through Isotropic medium
Refraction through Anisotropic medium
 Medium
Isotropic Anisotropic
When the properties of a material are When the properties of a material vary with
the same in all directions, the material different crystallographic orientations, the
is said to be isotropic. material is said to be anisotropic.

Substances such as gases, liquids,

glasses and amorphous solids have no Since the arrangement of particles is
long range order in them. Therefore, different along different directions in all
value of any of their physical property minerals (except those crystallizing in
would be same along any direction. isometric system), the value of the same
physical property is found to be different
Minerals that crystallize in the isometric along each direction. The velocity of light or
crystal system are isotropic. the refractive index varies with direction

The velocity of light or the refractive Snell’s law is not obeyed for random
index does not vary with direction in an orientations in anisotropic materials
isotropic substance. Anisotropic crystals can polarize light in
Snell's Law is obeyed by all isotropic certain directions (privileged directions).
materials.
 Double Refraction/ Birefringence
All anisotropic minerals exhibit the
phenomenon of double refraction.
When unpolarized light enters the
crystal from below, it is broken into
two polarized rays that vibrate
perpendicular to each other within
the crystal:

Ordinary ray, or o-ray (follows Snell’s law). The o-ray vibration direction is
perpendicular to the plane containing the c-axis and the path of the ray.

Extraordinary ray, or e-ray. (does not follow Snell’s law):The e ray is polarized
with light vibrating within the plane containing the c-axis and the propagation
path of the ray.
 o-ray and e-ray

Snell’s law: ni sin (i) = nr sin (r)

If the angle of incidence is 0o (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, since sin(0o) = 0, making sin (r) = 0, and resulting in r = 0.

Since the angle of incidence of the light is 0o, both rays should not be refracted when
entering the crystal according to Snell's Law, but the e-ray violates this law because
it's angle of refraction is not 0o, but is r.
Note that the vibration directions of the e-ray and the o-ray are perpendicular to each
other. These directions are referred to as the privileged directions in the crystal.
The o-ray has a vibration direction that is
perpendicular to the propagation
direction.

wave normal

The vibration direction of the e-ray is not perpendicular to the propagation

direction. A line drawn that is perpendicular to the vibration direction of the e-ray
is called the wave normal.
Although Snell’s Law is not satisfied by the ray path for extraordinary rays, it is
satisfied by the wave normals of extraordinary rays. In other words, the wave
normal direction for the refracted ray is related to the wave normal direction for
the incident ray by Snell’s Law.
 Polarizer

When 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