Chapter 24Wave OpticsInterferenceConditions for InterferenceProducing Coherent SourcesProducing Coherent Sources, contYoung’s Double Slit ExperimentYoung’s Double Slit Experiment, DiagramResulting Interference PatternFringe PatternInterference PatternsInterference Patterns, 2Interference Patterns, 3Interference EquationsInterference Equations, 2Interference Equations, 3Interference Equations, 4Interference Equations, finalUses for Young’s Double Slit ExperimentLloyd’s MirrorInterference Pattern from the Lloyd’s MirrorPhase Changes Due To ReflectionPhase Changes Due To Reflection, contInterference in Thin FilmsInterference in Thin Films, 2Interference in Thin Films, 3Interference in Thin Films, 4Interference in Thin Films, 5Interference in Thin Films, finalNewton’s RingsProblem Solving Strategy with Thin Films, 1Problem Solving with Thin Films, 2Problem Solving with Thin Films, 3Interference in Thin Films, ExampleCD’s and DVD’sCD’s and Thin Film InterferenceReading a CDReading a CD, contDVD’sDiffractionDiffraction, 2Diffraction, 3Fraunhofer DiffractionSingle Slit DiffractionSingle Slit Diffraction, 2Single Slit Diffraction, 3Single Slit Diffraction, 4Diffraction GratingDiffraction Grating, contDiffraction Grating, finalDiffraction Grating in CD TrackingPolarization of Light WavesPolarization of Light, contPolarization by Selective AbsorptionSelective Absorption, contSelective Absorption, finalPolarization by ReflectionPolarization by Reflection, contPolarization by ScatteringPolarization by Scattering, contOptical ActivityLiquid CrystalsLiquid Crystals, 2Liquid Crystals, 3Liquid Crystals, finalChapter 24Wave OpticsWave OpticsThe wave nature of light is needed to explain various phenomenaInterferenceDiffractionPolarizationThe particle nature of light was the basis for ray (geometric) opticsInterferenceLight waves interfere with each other much like mechanical waves doAll interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combineConditions for InterferenceFor sustained interference between two sources of light to be observed, there are two conditions which must be metThe sources must be coherentThey must maintain a constant phase with respect to each otherThe waves must have identical wavelengthsProducing Coherent SourcesLight from a monochromatic source is allowed to pass through a narrow slitThe light from the single slit is allowed to fall on a screen containing two narrow slitsThe first slit is needed to insure the light comes from a tiny region of the source which is coherentOld methodProducing Coherent Sources, contCurrently, it is much more common to use a laser as a coherent sourceThe laser produces an intense, coherent, monochromatic beam over a width of several millimetersThe laser light can be used to illuminate multiple slits directlyYoung’s Double Slit ExperimentThomas Young first demonstrated interference in light waves from two sources in 1801Light is incident on a screen with a narrow slit, SoThe light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S1 and S2Young’s Double Slit Experiment, DiagramThe narrow slits, S1 and S2 act as sources of wavesThe waves emerging from the slits originate from the same wave front and therefore are always in phaseResulting Interference PatternThe light from the two slits form a visible pattern on a screenThe pattern consists of a series of bright and dark parallel bands called fringesConstructive interference occurs where a bright fringe appearsDestructive interference results in a dark fringeFringe PatternThe fringe pattern formed from a Young’s Double Slit Experiment would look like thisThe bright areas represent constructive interferenceThe dark areas represent destructive interferenceInterference PatternsConstructive interference occurs at the center pointThe two waves travel the same distanceTherefore, they arrive in phaseInterference Patterns, 2The upper wave has to travel farther than the lower waveThe upper wave travels one wavelength fartherTherefore, the waves arrive in phaseA bright fringe occursInterference Patterns, 3The upper wave travels one-half of a wavelength farther than the lower waveThe trough of the bottom wave overlaps the crest of the upper waveThis is destructive interferenceA dark fringe occursInterference EquationsThe path difference, δ, is found from the tan triangleδ = r2 – r1 = d sin θThis assumes the paths are parallelNot exactly parallel, but a very good approximation since L is much greater than dInterference Equations, 2For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of the wavelengthδ = d sin θbright = m λm = 0, ±1, ±2, … m is called the order numberWhen m = 0, it is the zeroth order maximumWhen m = ±1, it is called the first order maximumInterference Equations, 3The positions of the fringes can be measured vertically from the zeroth order maximumy = L tan θ  L sin θAssumptionsL>>dd>>λApproximationθ is small and therefore the approximation tan θ  sin θ can be usedInterference Equations, 4When destructive interference occurs, a dark fringe is observedThis needs a path difference of an odd half wavelengthδ = d sin θdark = (m + ½) λm = 0, ±1, ±2, …Interference Equations, finalFor bright fringesFor dark fringes0, 1, 2brightLy m md    K10, 1, 22darkLy m md       KUses for Young’s Double Slit ExperimentYoung’s Double Slit Experiment provides a method for measuring wavelength of the lightThis experiment gave the wave model of light a great deal of credibilityIt is inconceivable that particles of light could cancel each otherLloyd’s MirrorAn arrangement for producing an interference pattern with a single light sourceWave reach point P either by a direct path or by reflectionThe reflected ray can be treated as a ray from the source S’ behind the mirrorInterference Pattern from the Lloyd’s MirrorAn interference pattern is formed The positions of the dark and bright fringes are reversed relative to pattern of two real sourcesThis is because there is a 180° phase change produced by