1From Last time…DiffractiongratingPlease pick up packof color sheetsThin-filminterferenceTwo-sourceinterference:Diffraction = interferencefrom many sourcesWave reflection from crystal• Interference of waves reflecting from different atomiclayers in the crystal.• Difference in path length ~ spacing between atomsside viewReflection fromtop planeReflectionfrom nextplaneX-raydiffractionpatternX-ray “diffraction”• Diffraction spot arrangement indicatesatomic arrangement• Used to determine atomicarrangements of complex molecules.– e.g. DNAMolecularstructureDiffraction: single slit interference• Huygen’s principle:each portion of theslit acts as a sourceof waves• These sourcesinterfere accordingto path-lengthdifference.Single slit diffraction pattern• Interference-like pattern froma single slit.Important parameter:! "/ aWavelength comparedto size of apertureLong wavelength:wide patternShort wavelengthnarrow patternOverlapping diffraction patterns• Two independent pointsources will produce twodiffraction patterns.• Too much overlap,resolution is lost.• Image shows two sourcesclearly resolved.θAngularseparation2Diffraction-limited resolutionEasily resolved(θ > θmin )• For a circular aperture (e.g. lens)diffraction limit(θ = θmin )not resolved(θ < θmin )! "min= 1.22#DWaves and geometry• Interference and diffraction demonstrate thatlight is a wave.• Doesn’t always appear as a straight ‘ray’ of light… but sometimes it almost does!Geometric optics:Tracing the path of light raysWhat is a light ray?• Light ray is a line in the direction alongwhich light energy is flowing.Ray enters eye -> you can see the light sourceWavefronts (crests of waves)What does a light ray do?• Light rays travel forever in straight lineunless they interact with matter(reflection, refraction, absorption)What about diffraction?• Light really behaves as a wave• The concept of a light ray is an approximationi.e. a lieWavelength << aperture size, rays are good approximationLight rays from point source• Light rays are not always parallel.– E.g. light bulb visible from all directions– Rays must be traveling in all directionsLight ray perpendicular to localwavefront (crest of wave).3Interaction of light with matterAbsorptionAnd all occursimultaneouslyReflectionRefractionReflection/refraction occur at interfaces between different materialsReflection and Refraction• Direction of light can be changed by– Reflection (lets you see an object)– Refraction (transmits light thru object) … at an interface between different materials• Ray is the incident ray• Ray is the reflected ray• Ray is refracted into thelucite• Ray is reflected inside thelucite• Ray is refracted as it entersthe air from the luciteAirPlasticInter-faceWhen are materials different?• For reflection/refraction– materials are different if they havedifferent index of refraction– Light propagates at different speedin different materials.– Due to interaction ofelectromagnetic wave with atomsin material.1.36Ethyl Alcohol1.59Polystyrene plastic1.66Flint glass2.41Diamond1.52Crown glass1.46Pyrex glass1.46Oil1.33Water1.31Ice1.00Air (accepted)1.0003Air (actual)1.00 exactlyVacuumIndexof refractionMaterial! v =cnc=speed of light in vacuumWhat do you think?Pyrex stirring rod (n=1.46) dipped into beaker ofWesson oil (n=1.46). What happens to the rod?Pyrexstirring rodA. Appears darkB. Appears brightC. Appears invisibleD. Appears curvedE. Appears invertedNo reflection/refraction if index of refraction is same.Beaker ofWesson oilReflection• Angle of incidence = angle of reflectionθiθrIncidentrayReflectedray• Multiple reflections• Apply θi=θr at each surface –trace rayWhy θi=θr?• Christian Huygens modeled this in 1690– Said that each point on wavefront acts as source ofspherical wavelets– Superposition of wavelets gives reflected planewave such that θi=θrθiθr4What about refraction?• Refraction occurs when light moves intomedium with different index of refraction.• Result: light direction bends according toSnell’s lawθi,1θrθ2Angle of refractionn1n2! n1sin"1= n2sin"2Why Snell?• Can analyze in exactly the same way• Light moves at different speed in different mediaθiθrn1n2>n1θ2v2<v1Refraction anglen2 < n1v2>v1Reflected rayn1n2 >n1v2<v1n1Reflected rayn2>n1Refracted ray benttoward normaln2<n1Refracted ray bentaway from normalslower in medium 2 faster in medium 2Quick quizWhich of these fluids has thesmallest index of refraction(highest light speed)?ABCA. Fluid AB. Fluid BC. Fluid CD. All equalNumerical ExampleA beam of light is traveling underwater, aimed up at thesurface at 45˚ away from the surface normal. Part ofit is reflected back into the water, and part istransmitted into the air.Watern1=1.33Airn2=1.00θ1=45˚! n1sin"1= n2sin"2sin"2=n1n2sin"1= 0.94"2= arcsinn1n2sin"1# $ % & ' ( = 70˚θ2Quick quizA trout looks up throughthe surface at thesetting sun, and at themoon directlyoverhead.He seesA. Moon directly overhead, sun ~ parallel to water surfaceB. Moon directly overhead, sun ~ 40˚ above water surfaceC. Moon ~ 40˚ from vertical, sun ~ parallel to water surfaceD. Moon and sun aligned at 40˚ from
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