Wave Nature of Light & Wave Nature of Light & Electromagnetic WavesElectromagnetic Waves

History, Light is a Wave & History, Light is a Wave & PolarizationPolarization

TermsTerms

Superposition: Algebraic sum of the Superposition: Algebraic sum of the displacements of waves.displacements of waves.

Interference: Pattern produced by Interference: Pattern produced by interfering waves, can be interfering waves, can be constructive or destructive.constructive or destructive.

Diffraction: The spreading of light Diffraction: The spreading of light beyond a barrier. (Huygens beyond a barrier. (Huygens principle applies)principle applies)

Conditions of InterferenceConditions of InterferenceBest if monochromatic – single Best if monochromatic – single

frequency, one color lightfrequency, one color lightCoherent – Constant phase relationship. Coherent – Constant phase relationship.

Same frequency and in phase. (variance Same frequency and in phase. (variance of one’s phase to the other is constant) of one’s phase to the other is constant)

Zero Phase difference “In Phase” – Zero Phase difference “In Phase” – ConstructiveConstructive

180180˚ difference in phase – out of phase ˚ difference in phase – out of phase by ½ by ½ λλ so it is destructive so it is destructive

RainbowsRainbows

Chromatic DispersionChromatic Dispersion Index of refraction is greater for a Index of refraction is greater for a

shorter wavelength (blue) than for a shorter wavelength (blue) than for a longer wavelength (red)longer wavelength (red)

Occurs with prisms where white light Occurs with prisms where white light is spread into its constituant colors.is spread into its constituant colors.

Christian Huygens 1678Christian Huygens 1678

Every point of a wave front may Every point of a wave front may be considered the source of be considered the source of secondary wavelets that spread secondary wavelets that spread out in all directions with a speed out in all directions with a speed equal to the speed of equal to the speed of propagation of the waves.propagation of the waves.

Thomas Young, 1801Thomas Young, 1801

Experiment demonstrated the wave Experiment demonstrated the wave nature of light and nature of light and

Allows one to determine the Allows one to determine the wavelength, wavelength, λλ of a beam of light of a beam of light

Measured the average wavelength of Measured the average wavelength of sunlight. (570 nm measured – sunlight. (570 nm measured – Current is 550 nm. Very close!)Current is 550 nm. Very close!)

Newton was wrongNewton was wrong

If light had been particles or If light had been particles or corpuscles as Newton considered corpuscles as Newton considered them, then it would pass directly them, then it would pass directly through the slits to the screen through the slits to the screen beyond in Young’s experiment.beyond in Young’s experiment.

This did not happen!This did not happen!

Phase difference can Phase difference can change…change…

The phase difference between two The phase difference between two waves can change if the waves travel waves can change if the waves travel paths of different lengths.paths of different lengths.

Path Length DifferencesPath Length DifferencesEqual to mEqual to mλλ - constructive & bright - constructive & bright

fringefringeEqual to ½mEqual to ½mλλ - destructive and dark - destructive and dark

fringe.fringe.

Interference from path Interference from path differencedifference

If If dd << << LL then the difference in path then the difference in path length travelled by the two rays is length travelled by the two rays is approximately: approximately: rr1 - 1 - rr2 2 ≈≈ ddsin sin θθ

Where Where θθ is approximately equal to the is approximately equal to the angle that the rays make relative to a angle that the rays make relative to a perpendicular line joining the slits to perpendicular line joining the slits to the screen. the screen.

Bright & Dark FringesBright & Dark Fringes

If the rays were in phase when they If the rays were in phase when they passed through the slits, then the passed through the slits, then the condition for constructive interference at condition for constructive interference at the screen is: the screen is: ddsinsinθθ = = mm λλ , ,mm = = ±±1, 1, ±±2,...2,...

The condition for destructive The condition for destructive interference at the screen:interference at the screen: d dsinsinθθ= (= (mm + + ½)½)λλ , ,mm = = ±±1, 1, ±±2,...2,...

Where m is the order of the interference Where m is the order of the interference fringe. (m=1 is on either side of the central fringe. (m=1 is on either side of the central fringe) fringe)

When y << LWhen y << L

sin sin θθ ≈≈ yy//LL (Your text uses x instead (Your text uses x instead of y)of y)

So y = So y = λλmL/dmL/d

Diffraction GratingDiffraction Grating

Large number of equally spaced Large number of equally spaced parallel slits.parallel slits.

Creates even sharper and narrower Creates even sharper and narrower bright maxima than Young’s Double bright maxima than Young’s Double Slit.Slit.

Useful for precise measurements of Useful for precise measurements of wavelengths.wavelengths.

Thin Film InterferenceThin Film Interference

Interference of light waves reflecting Interference of light waves reflecting off the top surface of a film with the off the top surface of a film with the waves reflecting from the bottom waves reflecting from the bottom surface surface

Examples of Thin Film Examples of Thin Film InterferenceInterference

CDCD

OilOil

Soap BubbleSoap Bubble

ElectromagnetismElectromagnetism

James Clerk Maxwell 1864James Clerk Maxwell 1864

Hypothesized that since a changing magnetic Hypothesized that since a changing magnetic field produces an electric field (Faraday’s Law) field produces an electric field (Faraday’s Law) the opposite could be true.the opposite could be true.

Worked out mathematically these described:Worked out mathematically these described:Charge Density and the Electric Field

The Structure of the Magnetic Field A Changing Magnetic Field and the Electric Field

The Source of the Magnetic Field The Source of the Magnetic Field

Leading to…Leading to…

Electric and magnetic fields acting together Electric and magnetic fields acting together could produce an electromagnetic wave could produce an electromagnetic wave which travels at the speed of light.which travels at the speed of light.

Prior to this, visible light was thought of as a Prior to this, visible light was thought of as a completely separate phenomenon. completely separate phenomenon.

Now light is understood to be an Now light is understood to be an electromagnetic waveelectromagnetic wave

His theory also implied that electromagnetic His theory also implied that electromagnetic waves were not limited to visible light.waves were not limited to visible light.

Heinrich Hertz, 1887Heinrich Hertz, 1887

First produced and observed EM First produced and observed EM waves in a laboratory setting using waves in a laboratory setting using LC circuit.LC circuit.

Observed energy transferObserved energy transferObserved normal wave behavior Observed normal wave behavior

such as reflection, refraction, such as reflection, refraction, interference, diffraction and interference, diffraction and polarization.polarization.

Hertz’s Experiment ShowedHertz’s Experiment Showed

Wave was produced in one circuit Wave was produced in one circuit and propagated across the room to a and propagated across the room to a second circuit.second circuit.

The wave moved at the speed of The wave moved at the speed of light!light!

Leading us to MarconiLeading us to Marconi

Guglielmo Marconi 1896 recognized Guglielmo Marconi 1896 recognized the implications of the EM wave the implications of the EM wave experiments.experiments.

Waves could be used for Waves could be used for communications, eliminating the need communications, eliminating the need for telegraph wires.for telegraph wires.

Radio SignalRadio SignalSent from Cornwall EnglandSent from Cornwall EnglandReceived in St. Johns NewfoundlandReceived in St. Johns Newfoundland

How does a turtle find a new How does a turtle find a new pond?pond?

PolarizationPolarization In general: The polarization of an EM In general: The polarization of an EM

wave refers to the direction of its wave refers to the direction of its electric field.electric field.

Light from the sun or an Light from the sun or an incandescent bulb is unpolarized.incandescent bulb is unpolarized.

How is light polarized…How is light polarized…

Pass a beam of light through a Pass a beam of light through a polarizer.polarizer.

Polarizer is a material that is Polarizer is a material that is composed of long thin electrically composed of long thin electrically conductive molecules oriented in a conductive molecules oriented in a specific direction.specific direction.

Reflected light is polarized Reflected light is polarized

PolarizerPolarizer

When unpolarized light hits a single When unpolarized light hits a single layer of polarizing material ½ the layer of polarizing material ½ the light goes through.light goes through.

If a second sheet is at a right angle If a second sheet is at a right angle to the first, no light will transmit to the first, no light will transmit through the second sheet.through the second sheet.

SourcesSources http://www.rare-earth-magnets.com/magnet_university/http://www.rare-earth-magnets.com/magnet_university/

maxwells_equations.htmmaxwells_equations.htm PhysicsPhysics, 4, 4thth Edition, Walker, James S.; Pearson Education, 2010. Edition, Walker, James S.; Pearson Education, 2010. http://physics.about.com/od/mathematicsofwaves/a/huygensprincipl.htmhttp://physics.about.com/od/mathematicsofwaves/a/huygensprincipl.htm http://www.mathpages.com/home/kmath242/kmath242.htmhttp://www.mathpages.com/home/kmath242/kmath242.htm http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

doubleslitjavafigure1.jpgdoubleslitjavafigure1.jpg http://www.daviddarling.info/images/Youngs_double-slit_experiment.jpghttp://www.daviddarling.info/images/Youngs_double-slit_experiment.jpg http://theory.uwinnipeg.ca/physics/light/node9.htmlhttp://theory.uwinnipeg.ca/physics/light/node9.html electron9.phys.utk.eduelectron9.phys.utk.edu http://images.google.com/imgres?imgurl=http://farm1.static.flickr.com/http://images.google.com/imgres?imgurl=http://farm1.static.flickr.com/

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