Pleochroism
- Some minerals absorb different λ’s of light depending on light vibration direction
- anisotropic minerals
- pleochroic uniaxial - color varies btwn 2 hues
- pleochroic biaxial - color varies btwn 3 hues
- occurs because absorption is a function of direction–the two rays of light are absorbed differently as they pass thru the mineral
- not related to birefringence
- may only be observed in PPL
Birefringence
- the property of having different indices of refraction in different directions
- anisotropic minerals
- occurs when the speed of light in the grain varies in different directions
- tested by observing a mineral in XPL and with the gypsum plate in, and rotate the stage
- birefringent minerals will display a diagnostic color range called interference colors
Interference Colors
- Occur b/c light waves passing thru xtals can have a variety of λ’s, A’s, and phases that are affected by atomic structure n different ways.
- in XPL there may be colors that are brighter and more pronounced than in PPL
- They result from the interference of light rays passing thru the upper polarizer
- determined by the difference in indices of refraction in the section
- Diagnostic b/c different minerals display different ranges of interference colors
- based on a formula determined by the grain orientation with respect to the vector direction of the polarized light and the thickness of the grain
Becke Lines
- Light interacts w/the mineral grain as if were a lense, so:
- If nmineral > nliquid then refracted rays converge
- If nmineral < nliquid then refractd rays diverge
- the result of 2 things:
- the fact that minerals in thin sections act like lenses
- internal reflection of light w/in the mineral is due to the presence of vertical grain boundaries
- used to look at the relief and determine the index of refraction of a mineral
- a band or rim of light visible along a grain or xtal boundary in PPL
- best seen in intermediate or low power
- the light becke line moves into the material of higher refractive index
Relief
Descibes the contrast btwn the mineral and its surroundings ==> as the difference btwn the RI of the liquid/mount and that of the mineral increases, the boundary btwn the two becomes more pronounced.
postive <==> negative
can you see the separation between the mineral and oil?
if the mineral has the higher RI –> positive relief
if the mineral has the lower RI –> negative relief
If the mineral and oil/mount differ substantially in their index of refraction, the mineral is said to stand out in “relief” and a dark line will appear around the mineral grain
Incident ray
the source light ray
generally splits into 2 rays when light passes from one material to another
Reflected ray
one of the two rays that split from the incident ray
the ray is reflected at the same angle that the incident ray entered the material
Refracted ray
- one of the two rays the split from the incident ray
- the ray that is transmitted thru the material but is bent
- how much the refracted ray is bent depends on 2 things:
- the difference in RI’s of the 2 materials
- the difference in densities of the 2 materials
Index of Refraction
The ratio of the velocity (v) of light in a vacuum to the velocity in the mineral:
n = vvacuum / vmineral
Depends on chemical composition, xtal structure, and bond type in the xtal
High values of n correspond to materials tha transmit light slowly
A mineral with a high value of n suggests that it is composed of atoms with high atomic #s, or of closely packed atoms
Critical Angle (θCA)
There exists some value of θi that will make θt = 90° ==> the limiting value of θi
If the angle of incidence (θi) > the critical angle (θCA) then none of the light will escape and the entire beam will be reflected inside the xtal
Snell’s Law can be rewritten:
θCA = nt / ni
Snell’s Law
The mathematical relationship between the angle of incidence (θi) and the angle of refraction (θr).
_ sin(θ_i) _ = _ vi _ _ = nr _ _
sin(θr) vr ni
therefore:
ni x sin(θi) = nr x sin(θr)
when ni < nt then θi > θt
when ni > nt then θi < θt
Opaque
a mineral will appear dark in both PPL, XPL, and while rotating the stage in XPL
Isotropic
Having the same properties in all directions, therfore:
a mineral may appear dark or transparent in PPL
a mineral will appear dark in XPL
nothing will happen when rotating the stage in XPL
Anisotropic
Having different optical properties in differernt directions, therefore:
a mineral may appear dark or transparent in PPL
a mineral may appear dark or transparent in XPL
when rotating the stage in XPL, a mineral will display changes in color and/or shade
- uniaxial minerals have 1 optic axis
- biaxial minerals have 2 optic axes
- when light passes thru a xtal’s optic axis, it appears isotropic, however the odds are low
Properties of Light
- Different colors of light are characterized by different wavelengths (λ)
- The intensity of a wave is proporional to its amplitude (A)
- The electric vectors of unpolarized light vibrate in all directions perpendicular to the direction of travel
- The electric vectors of PPL are constrained to vibrate in a single plane
- If λ’s corresponding to all of the primary colors are present with nearly equal intensity, the light appears white.
Polychromatic
many colored
ex: white light
Monochromatic
single colored
when only one λ is isolated
Constructive Interference
- when waves are in-phase
- no energy is lost
- waves are in-phase when their peaks and λ’s correspond, so they add to produe one wave w/twice the A
Destructive Interference
- when waves are out-of-phase, waves “consume” some or all of each other’s energy
- whn waves are completely out-of-phase, their motions cancel and addition leads to complete loss of energy
Dispersion
- The property that RI varies with λ
- can sometimes be see in thin section
- Dispersion affects luster
- high dispersion appears adamantine… ex: diamond
- low dispersion appears dull… ex: fluorite
Refraction
- Objects appear to bend as they pass from air into water
- Occurs when a beam of light passes from one medium to another w/a different RI
- The beam refracts toward the medium w/the higher RI
- A beam traveling 90° to the interface, is not refracted
Angle of Incidence (θi)
The angle between the incident ray and the normal to the surface.
Angle of Refraction (θr)
The angle between the refracted ray and the normal to the surface.
