13.1 Reflection and Refraction• Geometrical Optics• Reflection• RefractionChristian HuygensGeometrical opticsIn geometrical optics light waves are considered to move in straight lines.This is a good description as long as the waves do not pass through small openings (compared to λ)Light waves(surfaces with constant phase - e.g. maxima) perpendicularto wave frontsRays are not physicalentities but are aconvenient representationof a light wave.Wave frontRays are perpendicular to wave frontsReflection• Two general types of reflection– Specular reflection– Diffuse reflection• Most of geometric optics deals with specular reflection.• However, most of the time ambient lighting is due to diffuse reflection.Specular reflectionDiffuse reflectionFlat surfaceLight reflected in one directionRough surfaceLight reflected in all directions2Transmission and Reflection at an interfaceTransmissionReflectionAbsorptionxIncident wavemedium 1medium 1Specular ReflectionDiffuse reflection (scattering)TransmissionAbsorptionWhat are some examplesof these processes in this picture.Law of ReflectionThe angle of reflection equals the angle of incidenceAngle of incidenceAngle of reflection'11θ=θReflecting surfaceMultiple reflections• For multiple reflections use the law of reflection for each reflecting surface.2-Dimensional Corner reflectorShow that 2 perpendicular mirrors reflect a light beam in a plane perpendicular to both mirrors back along the opposite directionθ1θ1’θ’2θ2we want to show that 21'90θθ=−11'=θθ21'90+=oθθ21'90=−θθ22'=θθ90-θ121'90+=oθθMirror 2Mirror 1Refraction• Refraction is the bending of light when it passes across an interface between two materials. • The bending is due to the differences in the speed of light in different media.• The index of refraction of a material niis the ratio of the speed of light in a vacuum c to the speed of light in the material viiicnv=3Speed of light in a mediumWave in vacuumExcites oscillation of electrons in mediumSuperposition of waves leads to slower speed in the medium compared to vacuum.Transmission across an interfaceThe speed of the wavechanges.The frequency remainsthe same.The wavelength changesRefraction and ReflectionSnell’s Law of Refraction112 2n sin n sinθ= θn2 > n1θ2 < θ1(sinθ increases with θ )Going from air to glassGoing from glass to airn2 < n1θ2 > θ14Physical picture for Snell’s LawOne end of the wave front slows down.The wave front changes direction.Example 22.2Find the angle of refraction foran angle of incidence of 30oingoing from air to glass (nglass=1.52)112 2n sin n sinθ=θ1122nsinsinnθθ=1.00(sin30)0.331.52==o219.3θ=Example 22.4112 2n sin n sinθ= θShow that light going througha flat slab is not deviated in angle.First interfaceSecond interfaceangle of incidence = θ22233nsin nsinθ= θthen113 3n sin n sinθ= θsince n1=n3θ1=
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