Lecture 14 (11/13/2006)Lecture 14 (11/13/2006)

Analytical MineralogyAnalytical MineralogyPart 1:Part 1:

Nature of LightNature of LightIntroduction to Optical MineralogyIntroduction to Optical Mineralogy

Nature of LightNature of Light

Visible light is a form of Visible light is a form of electromagnetic electromagnetic radiationradiation, which can be characterized as , which can be characterized as pulses or waves of electrical energypulses or waves of electrical energy

Travels in straight lines with a transverse Travels in straight lines with a transverse wave motionwave motion

Unpolarized lightPolarized light

Attributes of LightAttributes of LightWavelength (Wavelength (distance between wave peaks; measured in distance between wave peaks; measured in

angstroms (Å); defines color of visible lightangstroms (Å); defines color of visible lightAmplitudeAmplitude ((AA) ) height of light waves; corresponds to the height of light waves; corresponds to the

intensity/brightness of lightintensity/brightness of lightFrequency (Frequency () ) number of light waves passing a fixed point per second; number of light waves passing a fixed point per second;

measured in cycles/secondmeasured in cycles/secondVelocity (Velocity (vv = = ··)); speed of light ; speed of light in a vacuum in a vacuum = = 3·103·101818 Å/sec = Å/sec = cc

e.g. for orange light in a vacuum, e.g. for orange light in a vacuum, Å, Å, = 5·10 = 5·1014 14 /sec/sec

Light slows down as it passes through denser substances. Because Light slows down as it passes through denser substances. Because the frequency of light never changes as it passes through different the frequency of light never changes as it passes through different substances, a decrease in light velocity reflects a proportional substances, a decrease in light velocity reflects a proportional decrease in its wavelength.decrease in its wavelength.

Electromagnetic SpectrumElectromagnetic Spectrum

From Bloss, 1961

Reflection and Refraction of LightReflection and Refraction of Light

When light passes from a low density medium (e.g. air) When light passes from a low density medium (e.g. air) into a higher density non-opaque medium (e.g. a mineral), into a higher density non-opaque medium (e.g. a mineral), part will be part will be reflectedreflected and part will be pass through, but be and part will be pass through, but be bentbent and slowedand slowed – – refracted.refracted.

Angle of Angle of reflectionreflection ( (r’r’) equals the incident angle () equals the incident angle (ii)) Angle of Angle of refractionrefraction ( (rr) will differ from the incident angle ) will differ from the incident angle

depending on the change in velocity between the two depending on the change in velocity between the two substancessubstances

Refractive Index and Snell’s LawRefractive Index and Snell’s Law

Index of Refraction –Index of Refraction – n n nnsubstancesubstance = c / v = c / vsubstancesubstance >1 >1light velocity in air ≈ light velocity in air ≈ cc, so , so nnairair ~ 1 ~ 1

Snell’s Law-Snell’s Law- predicts the angle of refraction predicts the angle of refraction at the interface of two substances with at the interface of two substances with different refractive indicies:different refractive indicies:

nnii sin sin i i = n= nrr sin sin r r

r r = sin= sin-1-1 (n (nii/n/nrr xx sin sin ii))

Critical Angle of RefractionCritical Angle of RefractionCritical incident angle Critical incident angle ii is where is where r r > 90> 90ºº; i.e. total ; i.e. total

reflectionreflectionii

criticalcritical = sin= sin-1-1 (n (nrr/n/nii xx sin sin 9090ºº););

e.g., for ne.g., for nii = 2, n = 2, nrr = 1; = 1; iicriticalcritical

= = 3030ºº

for nfor nii = 1.5, n = 1.5, nrr = 1; = 1; iicriticalcritical

= = 41.841.8ºº

Successive RefractionSuccessive Refraction

Refraction, Relief, and the Becke Refraction, Relief, and the Becke LineLine

ReliefRelief is the degree to which a phase stands is the degree to which a phase stands out from its surroundings and is an out from its surroundings and is an expression of the contrast in index of expression of the contrast in index of refraction refraction

dark outline

Becke Line Test Becke Line Test

From Bloss (1961)

DispersionDispersion Because Because nn is related to light velocity, which is is related to light velocity, which is

related to wavelength (related to wavelength (((vv = = ··)), different , different wavelengths of light will have different refraction wavelengths of light will have different refraction indicies within a particular substance indicies within a particular substance

Illuminating a mineral with white light may thus lead Illuminating a mineral with white light may thus lead to color dispersionto color dispersion

Polarization of LightPolarization of Light Light emanating from a Light emanating from a

point source vibrates in point source vibrates in all directions normal to all directions normal to the propagation the propagation directiondirection

Light can be polarized Light can be polarized (made to vibrate in one (made to vibrate in one plane) by selective plane) by selective absorption (OR) or by absorption (OR) or by reflectance (OL)reflectance (OL)

AnisotropyAnisotropy

Indicies of refraction can vary in all minerals Indicies of refraction can vary in all minerals (except those in the isometric system) (except those in the isometric system) depending on the orientation of light ray. depending on the orientation of light ray. Such minerals are said to be Such minerals are said to be anisotropicanisotropic. .

Isometric minerals, glass, liquids and gasses Isometric minerals, glass, liquids and gasses have a single refraction index value have a single refraction index value regardless of the orientation of light rays. regardless of the orientation of light rays. Such substances are said to be Such substances are said to be isotropicisotropic. .

Next Lecture 11/15/06Next Lecture 11/15/06

Optical Properties of Uniaxial MineralsOptical Properties of Uniaxial Minerals

Read: Read: Klein p. 298-303Klein p. 298-303Perkins and Henke, p. 14-22Perkins and Henke, p. 14-22