PHYSICS 2-3

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PHYSICS 2-3

The texts for this course are:1. H. D. Young & R. A. Freedman, UNIVERSITY

PHYSICS 10TH ed. 1999. 2. H. D. Young & R. A. Freedman, MODERN PHYSICS

11TH ed. 2003. 3. French, A.P. VIBRATIONS AND WAVES 1971. 4. Bekefi & Barrett, ELECTROMAGNETIC

VIBRATIONS, WAVES AND RADIATION 1977. 5. Asimov, I. Atom: JOURNEY ACROSS THE

SUBATOMIC COSMOS 1991.6. JUST SIX NUMBERS, Martin Rees, 2000.7. ? THE ASCENT OF SCIENCE OUP 2000.

Dr. BILL MILLS IS• The husband of one.• The father of 16 (including in-laws).• The grandfather of 8 so far.• A Christian Priest, Ecumenist, Theologian &

Apologist. A Physicist, and an International Attorney.

• Committed to responsible epistemology.• A positivist* 2

Opening remarks: WelcomeIntroductory class business:

I am not

Inerrant, infallible, nor immune from mere Scribner error.

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IN OPPOSITION OR IN HARMONY?

“Religion and science are opposed…but only in the same sense as that in which my thumb and forefinger are opposed- and between the two, one can grasp everything.” Sir William Bragg

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“Who can learn anything new and not find it a shock?” John Wheeler

It is helpful to regularly review even our most fundamental

understandings in light of our most recent discoveries.

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Religion and Science:Two Sides Of One Coin

Warm summer evenings in Greece in the 4th century B.C. Democritus¹: 460-370 B.C. “Atomic system” wandering lights in the night sky, (GK. “planetes”, “wanderers”). Stationary grains of sand on the sea shore, (“atomos”, “atoms” meaning “indivisible” or “unbreakable). Aristotle: 384-322 B.C. The father of science. Knowing the physical world inexorable leads to knowing the existence of God & His qualities. (“physika”, “physics”, Gk. “of nature”, “to bring forth”). Four elements, each with their unique place & duty in the universe² Everything held in it’s place, whether fixed or in motion, by eternal natural laws, ordained by God.

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INTRODUCTION

Measurement Standards & degrees of uncertainty:VECTORS & SCALARS:A scalar has only magnitude and no direction.A vector is a physical quantity that requires the specification of both direction and magnitude.

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Ordinal Set Theory

Mohamed Ali and superlatives: Someone is always “The Greatest”.In any defined group or set, for every measureable quality, one member of that group is “most” or “best”.If qualities can be summed, someone is the overall “greatest.”Of all beings currently conscious, one of them is the greatest, (using the Laws, Constants, Forces, & Elements most effectively to bless & serve others).That being is God.For Christians that living being is Jesus Christ!Agnostics & Atheists have simply not been persuasively or effectively introduced to Him, Yet!

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Epistemology How certain can I be?

“Any measurement that you make (decision that you come to) without knowledge of its uncertainty is completely meaningless.” “A measurement that doesn’t also indicate its degree of accuracy is meaningless.” “Knowing degrees of accuracy is critical to so many things in our lives.” Dr. Walter Lewin: FOR THE LOVE OF PHYSICS, 2011 pgs. x. ,8. (Parenthetical comment added.)

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UNITS & DIMENSIONSINTRODUCTION & OVERVIEW

FUNDAMENTAL UNITS OF THE S.I.

1. LENGTH = METER¹.2. MASS = KILOGRAMME².3. TIME = SECOND³.4. ELECTRIC CURRENT = AMPERE⁴.5. THERMODYNAMIC TEMPERATURE = °KELVIN⁵.6. AMOUNT OF SUBSTANCE = MOLE⁶.7. LUMINOUS INTENSITY = CANDELA⁷; cd.

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DERIVED UNITS OF THE S.I.

8. °Celsius¹.9. 2D & 3D Angle: Radian; rad & Steradian; st.10.Area & Volume: Metre squared; M² & cubed; M³.11.Velocity: Metre/second; m/s⁻¹.12.Acceleration: Metre/second²; m/s⁻².13.Density: Kilogramme/metre³; kgm⁻³.14.Mass rate of flow: Kilogramme/sec; kgs⁻¹.15.Volume rate of flow: Cubic metre/sec; m³s⁻¹.16.Moment of inertia: kg m².17. Momentum & Angular: kg m s⁻¹ & kg m² s⁻¹ .

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18. Force: Newton; kg m s⁻².19. Torque (Moment of Force): Newton Metre; NM.20. Work (Energy Heat): Joule; 1J = 1NM = 1kg m²s⁻².21. Power: Watt; 1w = 1J s⁻¹.22.Frequency: Hertz; Hz= waves/s⁻¹.23.Electric Charge: Coulomb; C = A s.24.Pressure: Pascal; Pa = kg/m s² = N/m² = J/m³.25. Pressure & Surface Tension: NM.26. Luminous flux: Lumen; lm = cd sr.27.Illumination: Lux; lx = lm m⁻².

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28.Electric potential difference: Volt; V = kg m²/s³ A = J/A s = J/C29. Electric resistance: Ohm; Ω = kg m²/s³A² = V/A.30.Electric conductance: Siemens; S = s³A²/kg m² = Ω⁻¹. 31.Electric capacitance: Farad; F =

A₂s⁴/kg m² = A s/V = C/V.32.Magnetic flux: Weber; Wb = kg m²/s²A V s. 33.Inductance: Henry; H = kg m²/s²A² = V s/A = Wb/A.34.Magnetic flux density (magnetic induction) : Tesla; T

= kg/s²A = V s/m².

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VARIATIONS OF THE S.I.

35. Energy: Erg; erg = g cm²/s² = 10⁻⁷ J. 36. Force: Dyne; dyn = g cm/s² = 10⁻⁵ N. 37. Viscosity: Poise; P = g/cm s = 10⁻¹ Pa s. 38. Kinetic¹ Viscosity: Stokes; St = cm²/s = 10⁻⁴m²/s.39. Length: Micron; μ = 10⁻⁴ cm = 10⁻⁶m.40. Length: Angstrom: Å = 10⁻⁸cm = 10⁻¹⁰m.41. Volume: Liter; l = 10³ cm³ = 1 dm³ = 10⁻³ m³.42. Mass: Tonne; t = 10⁶g = 10³kg.43. Pressure: Bar; bar = 10⁶ dyn/cm² = 10⁵ Pa.44. Concentration (Molarity):

M = 10⁻³ mol/cm³ = mol/liter = mol/dm³.

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MEASURING IN 3 DIMENSTIONS IN METERS:

Distance from earth to most remote known quasar: 1 * 10²⁶.“ “ “ “ “ “ “ Galaxy: 4 * 10²⁵.“ “ “ “ nearest galaxy (m-31): 2 * 10²².“ “ “ to nearest star: 4 * 10¹⁶.One light-year: 9 * 10¹⁵.Our Solar System: 1 *10¹⁵.Mean orbital radius of the earth: 2 * 10¹¹.A view of our earth & moon: 1 *10¹⁰.Mean distance from earth to moon: 4 * 10⁸.Mean radius of the earth: 6 * 10⁶.Typical altitude of orbiting satellite: 2 * 10⁵.

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MEASURING IN 3 DIMENSTIONS IN METERS:

Length of a football field: 9 * 10¹.A Human: 2 X .3 X .3. Length of a housefly: 5 * 10⁻³.Smallest dust particles: 1 * 10⁻⁴.Most cells in most living organisms: 1 * 10⁻⁵.Diameter of A water molecule: 1 * 10⁻⁸.Diameter of A hydrogen atom: 1 * 10⁻¹⁰.Diameter of an atomic nucleus: 1 * 10⁻¹⁴.Diameter of An Electron & a proton: 1 * 10⁻¹⁵.Diameter of SuperStrings: 1 * 10⁻²⁰.

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MEASURING IN THE 4TH

DIMENSTION: THE STREAM OF TIME IN SECONDS:

Lifetime of a proton: 1 * 10³⁹.Age of the Observable Universe: 5 * 10¹⁷.Age of the earth: 1 * 10¹⁷.Age of the Pyramid of Cheops: 1 * 10¹¹.U.S. Human Life Expectancy: 2 * 10⁹.Average age of a college student: 6 * 10⁸.One year: 3 * 10⁷.Length of a day: 9 * 10⁴. Interval between human heartbeats: 8 * 10⁻¹.Period of audible sound waves: 1 * 10⁻³.

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MEASURING IN THE 4TH

DIMENSTION: THE STREAM OF TIME IN SECONDS:

Period of concert-A tuning fork: 2 * 10⁻³.Period of typical radio waves: 1 * 10⁻⁶.Lifetime of a Muon: 2 * 10⁻⁶.Period of vibration of an atom in a solid: 1 * 10⁻¹³.Period of visible light waves: 2 * 10⁻¹⁵.Duration of a nuclear collision: 1 * 10⁻²².Time for light to cross a proton: 3 * 10⁻²⁴.Lifetime of most unstable particle (1989): 1 *10⁻²³.Plank’s Epoch: 1 *10⁻⁴³.

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MEASURING MASS IN KG:

OUR OBSERVABLE UNIVERSE: 1 * 10⁵².OUR MILKYWAY GALAXCY: 7 * 10⁴¹.OUR SUN: 2 * 10³⁰.EARTH: 6 * 10²⁴.OUR MOON: 7 * 10²².AN AVERAGE SHARK: 1 * 10².AN AVERAGE HUMAN: 7 * 10¹.AN AVERAGE FROG: 1 * 10⁻¹.AN AVERAGE MOSQUITO: 1 * 10⁻⁵.AN AVERAGE BACTERIUM: 1 * 10⁻¹⁵.A HYDROGEN ATOM: 1 * 10⁻²⁷.AN ELECTRON: 1 * 10⁻³¹.

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MEASURING ENERGY & POWEROUTPUT IN JOULES¹ & WATTS²:

SUNLIGHT IN ONE YEAR: 10³⁴ J.SUNLIGHT IN ONE YEAR: 10²⁶ W.EARTH’S ROTATIONAL KINETIC ENERGY: 10²⁹ J.EARTH’S DAILY INPUT OF SOLAR ENERGY: 10²² J.AN AVERAGE H BOMB 10¹⁷ J.100% CONVERSION OF 1 GRAMOM MATTER : 10 J.¹⁴WORLD’S CURRENT ENERGY CONSUMPTION: 10 W.¹³ONE BARREL OF OIL: 10 J.¹⁰ONE AVERAGE POWER PLANT: 10 . W.⁹ONE MEDIUM PIZZA: 10 J.⁷ONE D CELL BATTERY: 10 J.⁴ONE MOSQUITO PUSHUP: 10 J.⁻⁷FISSION OF ONE ATOM OF U-235: 10 J.⁻¹¹ONE PERSON: 100 W.

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LARGE NUMBERS & DIVERSE SCALES

“We are each made up of between 10²⁸ and 10²⁹ atoms. This ‘human scale’ is, in a numerical sense, poised midway between the masses of atoms and stars. It would take roughly as many human bodies to make up the mass of the Sun as there are atoms in each of us. But our Sun is just an ordinary star in the galaxy that contains a hundred billion stars altogether. There are at least as many galaxies in our Observable Universe as there are stars in a galaxy. More than 10⁷⁸ atoms lie within range of our telescope.” There are @ 3 * 10²⁷ stars.

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“Living organisms are configured into layer upon layer of complex structure. Atoms are assembled into complex molecules; these react, via complex pathways in every cell, and indirectly lead to the entire interconnected structure that makes up a tree, an insect or a human. We straddle the cosmos and the microworld-intermediate in side between the Sun, at a billion metres in diameter, and a molecule at a billionth of a metre.

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It is actually no coincidence that nature attains its maximum complexity on this intermediate scale: Anything larger, if it were a habitable planet, would be vulnerable to breakage or crushing by gravity.” “ We are vulnerable to viruses a millionth of a metre in length, and the minute DNA double-helix molecule encodes our total genetic heritage. And it‘s just as obvious that we depend on the Son for its power.

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Uni-verse or Cosmos?

• Are There Universal Laws, (Equations)?• Are There Universal Constants?• Are There Universal Elements?• Are There Universal Forces• We do not live in an (exclusively) material world! • We live in a Universe, with Eternal Laws,

Constants, Elements, (materials) and Forces.• They are the Typical God: Eternal, unchanging,

omniscient, omnipotent, & omnipresent!

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Electromagnetic Force EM= Δ x E = - ∂B/∂T.¹

• God uses the EM force to hold molecules together and to animate all life. It is the basis of all chemistry!

• Man uses the EM force for virtually all of his technology!In one short elegant concept, Michael Faraday, a

humble Christian bookbinder, with no formal education, “discovers” the one law that describes both the generator and the motor in a single line! Where did he get this knowledge? According to his testimony, the Christian God revealed this to him! And a great deal more!

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Electromagnetic Force EM= Δ x E = - ∂B/∂T.

Michael Faraday & James Maxwell were two of the greatest scientists of their generation, two of the greatest scientists of the 19th Century! Their discoveries in physics changed the world! (lights, TV, radio, phones, Computers, Electricity!) Faraday & Maxwell were very devout Christians. They were the pioneering giants of electromagnetism. Christians both, they credit Him, God, with revealing the nature of electromagnetism to them. Shall we ignore both from whom they learned it and how?

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Electromagnetic Force EM= Δ x E = - ∂B/∂T.

Build &/or use a Magneto to light a bulb, run a motor &/or feel an electric current.

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COULOMB’S LAW & CONSTANT

F = K x ( ⃓q₁⃓ x ⃓q₂ ⃓) /r².Or, F = K x ( ⃓q₁⃓ x ⃓q₂ ⃓)/d².

Coulomb Constant: C = k = 8.9875 x 10⁹ N x m²/C².One Ampere per second equals one Coulomb.

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ELECTRIC FIELDThe temperature or pressure in this room at various points may be thought of as temperature or pressure fields. These are scalar fields. Gravity is a vector field. All fundamental Forces have fields.The electric field is measured by the newton/coulomb: N/C.

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ELECTRIC FIELD& POLARIZATION

POLARIZATION is the separation of the positive & negative charges of a molecule by an external agent.In 1747 Benjamin Franklin was the 1st to observe that there is only one type of electricity present in all matter.

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GAUSS’ LAW Where, Where, Gauss’s law: The surface integral of the normal competent of electric displacement for magnetic flux over any closed surface in a dielectric is equal to the total electric charge enclosed.The flux law:

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E-FIELD: WORK. ENERGY & POTENTIAL

when molecules are out of electronic balance, potential energy exists. The electrical impulse travels at the speed of light, the electrons themselves bumping from atom to atom travel far slower.In 1897 J.J. Thomson discovered the electron & that atoms may on occasion have one or two extra or two few.Einstein discovered the photoelectric effect in 1905.

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E-FIELD: WORK. ENERGY & POTENTIAL

Newton & the true source of “free” energy:

“Colours, sweetness, bitterness, these exist by convention, in truth there are atoms and fields from Forces in the void.” Mills 2003.

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ELECTRIC CURRENTOHM’S LAW

Where I = current, V= potential difference & r = resistance.

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ELECTRIC CIRCUITS

Where P is the rate of energy transfer & ₐₑ are each end of the circuit.

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CONDUCTORS & INSULATORS

POLAR & NONPOLAR DIELECTRIC MOLECULES:Electromagnetism is one place Physics, Φ; Chemistry, Χ; & Biology meet. Chemical bonding is actually electromagnetic bonding. There are actually three types of molecular bonding:1. Ionic Bonds; M⁺M⁻ Between oppositely ions. A

classical magnet. 2. Covalent Bonds where two atoms share electrons.3. Van der Waals Bonds which in turn come in three

types:

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CAPACITANCE CAPACITORS STORE POTENTIAL ELECTRIC ENERGY IN A ELECTROSTATIC FIELD. ΔV = Vf – Vi = ΔPE/q.

Where V = volts, J = Joules, & C = Columbs.

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CAPACITANCEE-FIELDS IN MATTER

Capacitance was discovered by Faraday & described by Gauss: Where, Where, Gauss’s law: The surface integral of the normal competent of electric displacement for magnetic flux over any closed surface in a dielectric is equal to the total electric charge enclosed.The flux law:

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RC CIRCUITS: CAPACITORS AS CIRCUIT ELEMENTS

Charging equation:

Discharging equation:

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IONIZATION Bad Φ joke about 2 atoms talking.

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MAGNETIC FIELDSLORENTZ FORCE

The force experienced by a point charge q moving wit a velocity v in a field of magnetic induction B & in an electric field E.

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MAGNETIC FIELD SOURCESBIOT-SAVART’S LAW

Defines the intensity of magnetic flux density produced at a point a distance from a current carrying conductor: *.

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MAGNETIC FIELD AMPERE’S LAW

The magnetic field H in the neighborhood of a conductor, length, L; carrying current I; ∫Hdl = I.

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MAGNETIC FIELDS IN MATTER

Bohr magneton: μB = eħ/2mε = 9.274078 x 10¯²⁴ J/T.Nuclear magneton: μN = eħ/2mp = 5.0508248 x 10¯²⁷ J/T.

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MAGNETIC INDUCTION FARADAY’S LAW

IF A CIRCUIT CONTAINS N LOOPS AND THE FLUX CHANGES BY AN AMOUNT Δ𝝷 DURING A TIME ΔT, THE AVERAGE INDUCED EMF DURING THE TIME ΔT IS

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MAGNETIC INDUCTION LENZ’S LAW,

EDDY CURRENTS THE POLARITY OF THE INDUCE EMF IS SUCH THAT IT PRODUCES A CURRENT WHOSE MAGNETIC FIEL OPOESE THE CHANGE IN MAGNETIC FLUX THROUGH THE LOOP. That is, the induce current tends to maintain the original flux through the circuit.

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MAGNETIC INDUCTION

Gauss’ law for magnetism:

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FUNDAMENTAL FORCES ELECTRIC CHARGE & E.S. INDUCTION.Electromagnetic induction¹: (EM) ΔX E = -∂B/∂T. Faraday-Maxwell.¹”The total electromotive force acting around any closed path in space is equal to the rate of decrease of the magnetic flux linking the path. In this equation ΔX represents a mathematical operator, called the Curl, which when acting on the vector E produces three partial differential equations. E represents electric field, ∂B represents changes in the magnetic field, and ∂T represents changes in time. It is also stated as: = 0,

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AC CIRCUITS

Why alternating currents? It takes advantage of Faraday’s law of induction allowing us to use transformers to carry more power farther more efficiently.• The voltage varies with time: • Capacitive reactance: • Inductive reactance: • Impedance Z, is the sum of the effective opposition

to the current flow: • Ohm’s law relationship for the RC circuit:

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RL CIRCUITS

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LCR CIRCUITS

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DISPLACEMENT CURRENT &MAXWELL’S EQUATIONS

Where, Where, Gauss’s law: The surface integral of the normal component of electric displacement for magnetic flux over any closed surface in a dielectric is equal to the total electric charge enclosed.The flux law:

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EM WAVES: A REVIEW:

GAUSS’ LAW FOR ELECTRICITY: GAUSS’ LAW FOR MAGNETISM: FARADAY’S LAW OF ENDUCTION: AMPERE’S LAW:

Φ OF LIGHT PARTICLE-WAVES.IS LIGHT EARTHLY OR HEAVENLY?

MATERIAL PARTICLES OR ENERGY WAVES?• In 1665 Dr. Isaac newton Jr. produced the 1st

intentionally created man-made rainbow by shinning light through a glass prism. This tended to disprove the belief that heavenly light was white & colors were earthly pollutions. It was also the 1st scientific publication in English & not in the universal language of Latin: On Light.

• Because these colors seemed immaterial, not from earthly particles, Newton called his rainbow a “spectrum” of light, as in “specter” Latin for ghost.

Φ OF LIGHT PARTICLE-WAVES.• Snell’s Law: Light refracted at the surface:

Φ OF LIGHT PARTICLE-WAVES.• Huygens's principle: The assumption that every

element of a wave front acts as the source of new waves. This applies to any wave but is used mostly in optics.

Φ OF LIGHT PARTICLE-WAVES.• Thomas Young’s famous 1801 double-

slit experiment:• “Young let light fall on a surface containing two

closely adjacent slits. The wedge of light from each slit fell on a screen and overlapped, resulting in a pattern of stripes-bright bands and dim bands alternating.”¹ Light couldn’t be only particles

• Path difference: • Constructive interference: Phase Difference for

n = 1,2,3,… • Destructive interference: For m = 1,3,5…

Φ OF LIGHT PARTICLE-WAVES.• Reflection: On a rough surface light reflect in

various directions & is called diffuse reflection. On a smooth surface (like glass or water) the rays are parallel to each other & called specular reflection:

• • Refraction: • The Law of refraction:

Φ OF LIGHT PARTICLE-WAVES.Phase & group velocity:

• Vph = √ gλ/2π.• Vgr = ½ √ gλ/2π.

Φ OF LIGHT PARTICLE-WAVES.Wave solutions to Maxwell’s Equations:• Gauss’ Law for electricity¹: • Gauss’ Law for magnetism²: • Faraday’s Law³: • Ampere-Maxwell Law⁴: • μ₀ε₀ dφₑ/dt + μ₀i.

Φ OF LIGHT PARTICLE-WAVES.Polarization:

• In Britain TV antennas are/were vertical. In the U.S. they are/were horizontal. Public broadcast EM signals are arbitrarily polarized for better reception. Sunlight is not.

• Light maybe polarized by selective absorption.• Light maybe polarized by reflection.• Brewster’s Law: sin Θp/cos Θp – tan Θp. • Law of Malus: • Light maybe polarized by double refraction.• Light maybe polarized by scattering.

Φ OF LIGHT PARTICLE-WAVES.

• Rayleigh Scattering: Light reflected by fine particles suspended in the air.


• Fraunhofer diffraction: Occurs when rays reach a pint @ parallel.


• Fresnel diffraction: Occurs when rays reach a pint and are not parallel.

Φ OF LIGHT PARTICLE-WAVES.• Interference & thin films: Oil on water:• There is an 180° phase change upon reflection when

the reflecting medium has a higher index of refraction than the medium in which the wave is traveling: Where λ is the wavelength of light in free space.

Newton’s rings: Newton used this method to check the smoothness & uniformity of optical mirrors & lenses placing a thin air wedge between two optical surfaces. Optimally there will be an interference pattern of concentric bright & dark circular fringes, Newton’s rings. We still use them today.

Φ OF OPTICAL INSTRUMENTS.THE Φ OF TELESCOPES

& MICROSCOPES .• HOW DO TELESCOPES MAKE BIG FARAWAY THINGS

SEEM CLOSER?• HOW DO MICROSCOPES MAKE SMALL THINGS

SEEM BIGGER?• WHY DID COOK & LEEUWENHOEK CALL THE BASIC

UNIT OF ALL LIFE “CELLS”? • WHY DID LEEUWENHOEK DISCOVER ABOUT HIS

SEEDS?

Φ OF LIGHT PARTICLE-WAVES.• Diffraction Gratings are used to analyze light

sources. They can be made by scratching parallel lines on a glass plate. A typical grating might contain 5,000 lines per cm.

• For n = 0,1,2,3… Interference maxima for a grating.• LIGHT AMPLIFIED BY SIMULTANIOUS EMISSION OF RADIATION = LASER• A source of intense monochromatic light inclusive of the ultraviolet-visible-infrared regions.• Electrons within solids, liquids & gasses have been

used as lasing materials.

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WEB SITES OF INTEREST1. The Electronic Nobel Museum Project:

www.nobel.se/prize/index.html.2. www.aip.org.3. http://physics.nist.gov/euu/Constants/CODA recommended values of the fundamental physical constants4. www.isinet.com/.5. http://Webbook.nist.gov/.6. www.nist.gov/srd/jperd.htm. Cumulative index

to the Journal of physical and Chemical Reference Data.

7. Most college & university libraries.

http://www.nobel.se/prize/index.html

http://www.aip.org/

http://physics.nist.gov/euu/Constants/

http://www.isinet.com/

http://webbook.nist.gov/

http://www.nist.gov/srd/jperd.htm

PHYSICS 2-3

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