Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf ·...

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Optical Properties of Materials Nature of Light Light is an electromagnetic wave or photon. The magnetic and the electric field are perpendicular to each other. The velocity of light is c = 3 x 10 8 m/s c = 1 ε o µ o Speed of light related to electric permittivity and magnetic permeability

Transcript of Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf ·...

Page 1: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties of MaterialsNature of LightLight is an electromagnetic wave or photon. The magnetic and the electric field are perpendicular to each other. The velocity of light is c = 3 x 108 m/s

c =1

εoµo

Speed of light related to electric permittivity and magnetic permeability

Page 2: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

E = hν = h c / λE = hν = h c / λ

h: Planck’s constant6.63x10-34 J-s

Photons

Page 3: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

UV 100-400 nm 12.4 - 3.10 eVViolet 400-425 nm 3.10 - 2.92 eVBlue 425-492 nm 2.92 - 2.52 eVGreen 492-575 nm 2.52 - 2.15 eVYellow 575-585 nm 2.15 - 2.12 eVOrange 585-647 nm 2.12 - 1.92 eVRed 647-700 nm 1.92 - 1.77 eVNear IR 10,000-700 nm 1.77 - 0.12 eV

Page 4: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Electromagnetic Radiation and the Visible SpectrumIf absorbance occurs in one region of the color wheel the material appears with the opposite (complimentary color). For example: a material absorbs violet light

→ Color = Yellowa material absorbs green light

→ Color = Red a material absorbs violet, blue & green

→ Color = Orange-Reda material absorbs red, orange & yellow

→ Color = Blue

RedRed

OrangeOrange

YellowYellow GreenGreen

BlueBlue

VioletViolet

( ) ( )

nm E (eV)

s m x . eV-s x . λ

hc E -

λ

λ1240

1099821013574 1815

=

×==

−.

Page 5: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Light Interaction with SolidsIncident light is either reflected, absorbed, or transmitted:

RATo IIII ++=

Incident: Io

Reflected: IR Absorbed: IA

Transmitted: IT

Optical classification of materials:

T + A + R = 1

T = IT /I0 Transmissivity

A = IA /I0 Absorptivity

R = IR /I0 ReflectivityTransparent

Transluscent

Opaque

T~1 : TransparentT~0 : Opaque

Page 6: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical phenomena involveinteractions between lightand atoms, ions, and/or electrons.

Optical phenomena involveinteractions between lightand atoms, ions, and/or electrons.

Page 7: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties & Band Structure• Reflection

– Scattering at an interface between two materials w/ different n

• Absorption– Electronic Polarization– Electron excitation to defect levels in the band gap– Electron excitation across the band gap

Metal

filledempty

Insulator

filled

empty

filled

empty

Semiconductor

Valence Band

Conduction Band

Page 8: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

AbsorptionAbsorption 1. Electronic polarization metals

2. Band transition Insulators and semiconductorshν > EgVisible light: 0.4 ~ 0.7µm in wavelength or

3.1 ~ 1.8eV

Page 9: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties of MetalsOptical Properties of Metals

Absorption of photons by electron transition:

∆E=hν∆E=hν Metals have a fine succession of energy states.Near-surface electrons absorb visible light.

Photons are used to excite the electrons to higher states (absorbed within 0.1µm and remitted in the form of visible light).

Page 10: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties of MetalsOptical Properties of Metals

Reflection: Electron transitionemits a photon.

re-emitted photon from material surface

• Reflectivity = IR/Io is between 0.90 and 0.95.• Reflected light is same frequency as incident.• Metals appear reflective (shiny)!

R is about 0.9~0.95R is about 0.9~0.95For visible light

Page 11: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Absorption and Reflectivity in MetalsMetals have a fine succession of energy states.Near surface electrons absorb visible light. Absorption of photons by electron transitions.Electron transition emits a photon.Reflectivity = IR/IO is between 0.90 and 0.95. Reflected light is same frequency as incident. Metals appear reflective (shiny)!

E = hν = h c / λE = hν = h c / λ

Incident photon energy

h = Planck’s constant (6.63x10-34J.s-1)

Page 12: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Why are Metals Shiny?• Metals Eg = 0 eV• All light with λ above X-ray wavelengths absorbed by continuous # of

unoccupied states above Ef.• Light is reemitted with exact energy of absorption as electrons fall

back into lowest state. Metals appear reflective as the light we see is reemitted.

Ef

absorption emission

Page 13: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties of Ceramics• What if the band gap is very large?

EGAP > Elight - there will be no absorption

What is the minimum value of Eg that that will let all visible light pass?

Egap> hυ=hc/λ for λ = 0.4 µm (min. visible wavelength)

Answer: Egap> 3.1eV

For ceramics with a large band gap - no absorption(Most insulating ceramics should be transparent!)

Page 14: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

• Absorption by electron transition occurs if hν > Egap

Selected Absorption: Insulators/SemiconductorsOptical Properties of NonmetalsOptical Properties of Nonmetals

Energy of electron

filled states

unfilled states

Egap

Io

blue light: hν= 3.1eV

red light: hν= 1.7eV

incident photon energy hν

• If Egap < 1.8eV, full absorption; color is black (Si, GaAs)• If Egap > 3.1eV, no absorption; colorless (diamond)• If Egap in between, partial absorption; material has a color.

Page 15: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Band to Band Transitions Optical Properties of

SemiconductorsOptical Properties of NonmetalsOptical Properties of Nonmetals

•We can examine the relationship between bonding (spatial and energetic overlap) and optical properties by considering the band-gaps of those compounds which adopt the Sphalerite/ Diamond structure, with all ions in tetrahedral coordination•(see figure to the right).

•Since electronic transitions from the valence to conduction band span a fairly large range of energies, semiconductors act as sort of a long pass filter (only reflecting light with energy less than the band gap). This can give rise to only certain colors.

Band Gap (Band Gap (eVeV)) ColorColor ExampleExample> 3.0 White ZnO3.0-2.5 Yellow CdS2.3-2.5 Orange1.8-2.3 Red HgS< 1.8 Black CdSe

Page 16: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Absorption by electron transition occurs if hν > EgapIf Egap < 1.8eV, full absorption; color is black (Si, GaAs)If Egap > 3.1eV, no absorption; colorless (diamond)If Egap in between, partial absorption; material has a color.

Selected Absorption: Insulators/Semiconductors

E = hν = h c / λE = hν = h c / λ

Incident photon energy

h = Planck’s constant (6.63x10-34J.s-1)

Page 17: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Can a light with a larger wave length interacts with a material with a large band gap?

Yes! through impurities.

x0T eII β−= ''

Generateheat

β: absorption coef.

Page 18: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

• Color determined by sum of frequencies of--transmitted light,--re-emitted light from electron transitions.

• Ex: Cadmium Sulfide (CdS)-- Egap = 2.4eV,-- absorbs higher energy visible light (blue, violet),-- Red/yellow/orange is transmitted and gives it color.

• Ex: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3-- Sapphire is colorless

(i.e., Egap > 3.1eV)-- adding Cr2O3 :

• alters the band gap• blue light is absorbed• yellow/green is absorbed• red is transmitted• Result: Ruby is deep

red in color.

40

60

70

80

50

0.3 0.5 0.7 0.9

Tra

nsm

itta

nc

e (

%)

Ruby

sapphire

wavelength, λ (= c/ν)(µm)

RedRed

OrangeOrange

YellowYellow GreenGreen

BlueBlue

VioletViolet

Color of NonMetals

Adapted from Fig. 21.9, Callister 6e. (Fig. 21.9 adapted from "The Optical Properties of Materials" by A. Javan, Scientific American, 1967.)

Page 19: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

COLORS in CeramicsColor is determined by sum of frequencies of (a) transmitted light and (b)

re-emitted light from electron transitions. Color is the result of the combination of wavelengths that are transmitted

Absorbed radiation can be reemitted as excited electrons drop back into original positions - not necessarily the same frequency as that absorbed

Small differences in composition can lead to large differences in appearance. Specific impurities can introduce electron levels within the band-gap - leads to color

For example, high-purity single-crystal Al2O3 is colourless sapphireIf we add only 0.5 - 2.0% of Cr2O3 we find that the material looks red rubyThe Cr substitutes for the Al and introduces impurity levels in the band gap

of the sapphire. These levels give strong absorptions at:400nm (green) and 600nm (blue) leaving only red to be transmitted

Page 20: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

SaphireBe3Al2SiO6

BerylBerylBeBe33AlAl22SiSi66OO1818

Page 21: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Color in Extended Inorganic Solids: Absorption

Intra-tomic (Localized) excitationsCr3+ Gemstones (i.e. Cr3+ in Ruby and Emerald)Blue and Green Cu2+ compounds (i.e. malachite, turquoise)Blue Co2+ compounds (i.e. Al2CoO4, azurite)

Charge-transfer excitations Fe2+ → Ti4+ in sapphireFe2+ → Fe3+ in Prussian BlueO2- → Cr6+ in BaCrO4

Valence to Conduction Band Transitions in SemiconductorsWO3 (Yellow)CdS (Yellow) & CdSeHgS (Cinnabar - Red)/ HgS (metacinnabar - Black)

Intraband excitations in MetalsStrong absorption within a partially filled band leads to metallic lustre or black colorationMost of the absorbed radiation is re-emitted from surface in the form of visible light

high reflectivity (0.90-0.95)

Page 22: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Intra-tomic (Localized) excitationsA similar technique is used to colour glasses or pottery glaze by adding impurities into the molten state:

Cu2+: blue-green, Cr3+: greenCo2+: blue-violet, Mn2+: yellowExample: If we take one mineral, beryl, and add different impurities, we get different colors: Beryl containing iron (Fe): Aquamarine = Fe++, beryl is blueHeliodor = Fe+++, yellowGreen beryl : due to mixtures of Fe2+ and Fe3+ Beryl containing Manganese(Mn):Morganite : Mn++ is pinkRed beryl : Mn+++ is redBeryl containing Chromium(Cr):Emerald = emerald green : Cr+++ From the above examples it is clear that the oxidation state (e.g., Fe2+ vs. Fe3+) also affects the color! . If impurity ions produce color, the color can be changed if the oxidation state can be changed.

Page 23: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Charge-transfer excitationsCharge transfer can only occur in compounds that have at least two elements in different and variable oxidation states. Charge transfer can produce very intense colors in gems and minerals. The term charge transfer refers to the process where electrons are swapped between elements.Examples of elements that can participate in charge transfer are: Fe2+ and Fe3+ ; Ti3+ and Ti4+ ; Mn2+ and Mn3+ and Mn4+ etc. Furthermore, a crystal can contain mixtures of these elements (e.g,. Mn and Fe) and these can participate in charge transfer. Energy is absorbed from visible light to transfer electrons from one atom to another.For example: A crystal contains metals (M) in two oxidation states: M2+ and M4+ . M2+ can loose an electron and become M3+ . M4+ can accept the electron (from above) and become M3+.Thus, the crystal can exist with M3+ plus M3+ or M2+ plus M4+. As you can see, these pairs are interchangeable by movement of an electron.

Page 24: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical Properties of NonmetalsOptical Properties of NonmetalsThe index of refraction n of a material is defined as the ratio of the velocity in a vacuum c to the velocity in the medium ν

Refraction: n = c/vn = c/v The speed of light is smaller in the materials

Index of refraction

εµ= /1vε: permittivityµ: permeability

rrr00v

cn ε≈µε=µε

εµ==

The larger atoms or ions the smaller ν and larger n

n is the same for all directions for cubic structures. For an anisotropic structure, n is higher in the direction of higher density of ions.

Relative magnetic permeabilityDielectric constant ε = permittivityµ = permeabilityo - “in a vacuum”r - “relative”

Since most of the substances are only slightly magnetic, µr ~ 1

Page 25: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

REFRACTION -OVERVIEW• Transmitted light distorts electron clouds.

+no

transmitted light

transmitted light +

electron cloud distorts

• Result 1: Light is slower in a material vs vacuum.

MaterialLead glassSilica glassSoda-lime glassQuartzPlexiglasPolypropylene

n2.11.461.511.551.491.49

--Adding large, heavy ions (e.g., leadcan decrease the speed of light.

--Light can be"bent"

Selected values from Table 21.1,Callister 6e.

materialainlightofspeedvacuuminlightofspeednefractionIndex_of_r_____

____==

• Result 2: Intensity of transmitted light decreases with distance traveled (thick pieces less transparent!)

Page 26: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Refraction is the bending of the path of a light wave as it passes from one material to another material.

The refraction occurs at the boundary and is caused by a change in the speed of the light wave upon crossing the boundary.

The tendency of a ray of light to bend one direction or another is dependent upon whether the light wave speeds up or slows down upon crossing the boundary.

Like any wave, the speed of a light wave is dependent upon the properties of the medium. In the case of an electromagnetic wave, the speed of the wave depends upon the optical density of that material.

The optical density of a medium is not the same as its physical density. The physical density of a material refers to the mass/volume ratio. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense which a material is, the slower that a wave will move through the material.

Page 27: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

For transparent materials - there is a relationship between index of refraction and dielectric constant! (The electrical properties and the optical properties of a material are related!)

For most ceramics, µr = 1(only slightly magnetic)

n ≅ εr

Page 28: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

The table below lists index of refraction values for a variety of medium. The materials listed at the top of the table are those through which light travels fastest; these are the least optically dense materials. The materials listed at the bottom of the table are those through which light travels slowest; these are the most optically dense materials. So as the index of refraction value increases, the optical density increases, and the speed of light in that material decreases.

<--highest optical density3.50Gallium phosphide

2.907Rutile

2.417Diamond

1.923Zircon

1.66Dense Flint Glass

1.58Light Flint Glass

1.52Crown Glass

1.51Plexiglas

1.36Ethyl Alcohol

1.333Water

1.31Ice

1.0003Air

<--lowest optical density1.0000Vacuum

Index of RefractionMaterial

Page 29: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

ReflectivityReflectivity R=IR /I0 ReflectivityReflection occurs at the interface between two materials and is therefore related to index of refractionReflectivity, R = IR/I0, where the I’s are intensitiesAssuming the light is normally incident to the interface: where n1and n2 are the indices for the two materials

2

12

12

nnnnR

+−

=

Typical glass: R=0.05Semiconductor with n=3: R=0.25

n2n1If 1 is airI0

n1

IR 2

2

2

1n1nR

+−

=n2

So, large n, larger R (brighter)Lenses coated with MgF2 to reduce reflection loss!Some lenses have multiple coatings for different wavelength

Page 30: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Emission of LightThe optical properties of extended solids are utilized not only for their color, but also for the way in which they emit light.

Luminescence – Emission of light by a material as a consequence of it absorbing energy. There are two categories:

Fluorescence: Emission involves a spin allowed transition (short excited state lifetime)

Phosphorescence: Emission involves a spin forbidden transition (long lived excited state).

Luminescence can also be classified according to the method of excitation:Photoluminescence: Photon excitation (i.e. fluorescent lights)Cathodoluminescence: Cathode rays (TV & Computer displays)Electroluminescence: Electrical injection of carriers (LED’s)

Page 31: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Energy of electron

filled states

unfilled states

Egap

re-emission occurs

• Process:

Adapted from Fig. 21.5(a), Callister 6e.

electron transition occurs

Energy of electron

filled states

unfilled states

EgapIncident radiation

emitted light

Application: LUMINESCENCE

• Ex: fluorescent lamps

UV radiation

coating e.g., β-alumina doped w/Europium

“white” lightglass

Ex: Picture on TV- inside of screen is coated with material that fluoresces when impinged on by electron beam

Page 32: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Application: PHOTOCONDUCTIVITY• Description:

Incident radiation

semi conductor:

Energy of electron

filled states

unfilled states

Egap

+

-A. No incident radiation: little current flow

Energy of electron

filled states

unfilled states

Egap

conducting electron

+

-B. Incident radiation: increased current flow

• Ex: Photodetector (Cadmium sulfide)

Page 33: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Optical CommunicationOptical Communication Application: FIBER OPTICS

2 optical fibers (0.1kg) can transmit 24000 calls (equivalent to 33tons of copper wires)

High-purity glass(5~100µ)

Human hair

Page 34: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Broaderoutput

Step-Index DesignStep-Index Design Near the interface, longer travel distance

• Design with stepped index of refraction (n):core: silica glass w/higher n

cladding: glass w/lower n∆n enhances internal reflection

inte

nsi

ty

time

input pulse

broadened!

inte

nsi

ty

time

output pulsetotal internal reflection

shorter pathlonger paths

Page 35: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

Near the surface, light travels faster.

B2O3 or GeO2

Graded-Index DesignGraded-Index Design

Sharperoutput

• Design with parabolic index of refractioncore: Add graded impurity distrib. to make n higher in core center

cladding: (as before)

total internal reflection

shorter, but slower paths longer, but faster paths

inte

nsi

ty

time

input pulse

inte

nsi

ty

time

output pulse

less broadening!

• Parabolic = less broadening = improvement!

Page 36: Optical Properties of Materials - UPRMacademic.uprm.edu/pcaceres/Courses/MatEng3045/EME7-1.pdf · Optical Properties of Materials Nature of Light Light is an electromagnetic wave

• When light (radiation) shines on a material, it may be:--reflected, absorbed and/or transmitted.

• Optical classification:--transparent, translucent, opaque

• Metals:--fine succession of energy states causes absorption and reflection.

• Non-Metals:--may have full (Egap < 1.8eV) , no (Egap > 3.1eV), or partial absorption (1.8eV <

Egap = 3.1eV).--color is determined by light wavelengths that are transmitted or re-emitted from

electron transitions.--color may be changed by adding impurities which change the band gap

magnitude (e.g., Ruby)• Refraction:

--speed of transmitted light varies among materials.

SUMMARY