From Last time…Single slit diffractionDiffraction: single slit interferenceOverlapping diffraction patternsDiffraction-limited resolutionWaves and geometryWhat is a light ray?What does a light ray do?What about diffraction?Light rays from point sourceInteraction of light with matterReflection and RefractionWhen are materials different?What do you think?ReflectionWhy i=r?What about refraction?Why Snell?Refraction angleQuick quizNumerical ExampleSlide 22Total Internal ReflectionOptical FibersFrom Last time…Diffraction grating Please pick up pack of color sheetsThin-film interference Two-source interference: Diffraction = interference from many sourcesSingle slit diffraction•Interference-like pattern from a single slit.Important parameter:€ λ/ aWavelength compared to size of apertureLong wavelength:wide patternShort wavelengthnarrow patternDiffraction: single slit interference •Huygen’s principle: each portion of the slit acts as a source of waves•These sources interfere according to path-length difference.Overlapping diffraction patterns•Two independent point sources will produce two diffraction patterns.•Too much overlap, resolution is lost.•Image shows two sources clearly resolved.AngularseparationDiffraction-limited resolutionEasily resolved( > min )• For a circular aperture (e.g. lens)diffraction limit( = min )not resolved( < min )€ θmin= 1.22λDWaves and geometry•Interference and diffraction demonstrate that light 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 along which 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 line unless 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 local wavefront (crest of wave).Interaction of light with matterAbsorptionAnd all occur simultaneouslyAnd all occur simultaneouslyReflectionRefractionReflection/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 the lucite•Ray is reflected inside the lucite•Ray is refracted as it enters the air from the luciteAirPlasticInter-faceWhen are materials different?•For reflection/refraction–materials are different if they have different index of refraction–Light propagates at different speed in different materials.–Due to interaction of electromagnetic wave with atoms in material.Material Index of refractionVacuum 1.00 exactlyAir (actual) 1.0003Air (accepted) 1.00Ice 1.31Water 1.33Ethyl Alcohol 1.36Oil 1.46Pyrex glass 1.46Crown glass 1.52Polystyrene plastic 1.59Flint glass 1.66Diamond 2.41€ v =cnc=speed of light in vacuumWhat do you think?Pyrex stirring rod (n=1.46) dipped into beaker of Wesson oil (n=1.46). What happens to the rod?Pyrex stirring rodA. Appears darkB. Appears brightC. Appears invisibleD. Appears curvedE. Appears invertedNo reflection/refraction if index of refraction is same.Beaker of Wesson oilReflection•Angle of incidence = angle of reflectionirIncidentrayReflectedray• Multiple reflections• Apply i=r at each surface –trace rayWhy i=r?•Christian Huygens modeled this in 1690–Said that each point on wavefront acts as source of spherical wavelets–Superposition of wavelets gives reflected plane wave such that i=r irWhat about refraction?•Refraction occurs when light moves into medium with different index of refraction.•Result: light direction bends according to Snell’s lawi,1r2Angle of refractionn1n2€ n1sinθ1= n2sinθ2Why Snell?•Can analyze in exactly the same way•Light moves at different speed in different mediairn1n2>n12v2<v1Refraction anglen2 < n1v2>v1Reflected rayn1n2 >n1v2<v1n1Reflected rayn2>n1Refracted ray bent toward normaln2<n1Refracted ray bent away from normalslower in medium 2 faster in medium 2Quick quizWhich of these fluids has the smallest 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 the surface at 45˚ away from the surface normal. Part of it is reflected back into the water, and part is transmitted into the air.Watern1=1.33Airn2=1.001=45˚€ n1sinθ1= n2sinθ2sinθ2=n1n2sinθ1= 0.94θ2= arcsinn1n2sinθ1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟= 70˚2Quick quizA trout looks up through the surface at the setting sun, and at the moon directly overhead. 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 vertical.n2=1.0n1=1.33Total Internal Reflection •Is possible when light is directed from n1 > n2 refracted rays bend away from the normal•Critical angle: angle of incidence that will result in an angle of refraction of 90° (sin = 1)For water:€ sinθc=11.333= 0.75 ⇒ θc= 48.75˚Optical FibersThe cladding has a lower n than the core•Plastic or glass light pipes•Applications:–Medicine: endoscope (light can be directed even if bent and the surgeon can view areas in the body using a
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