13.3 Reflection and Refraction II•Huygen’s Principle•Total internal refraction•DispersionWavesplane wavessphericalwavesBarrierHuygen’s Principle• All points in a given wave front are taken as point sources for the production of spherical secondary wavelets which propagate in space. After some time the new wave front is the tangent to the wavelets.Huygen’s Picture of a Plane waveHuygen’s Picture of a Spherical waveHuygen’s Explanation of Reflection•θ1= θ’12Huygen’s explanation for Refraction•n1sinθ1=n2sinθ2Fig. 22-24b, p.741Total Internal ReflectionWhen the angle of refraction equals or exceeds 90oAll the light isinternally reflectedTotal Internal ReflectionOptical Fiber -Light PipeAn optical fiber (light pipe) confines the light inside thematerial by total internal reflection. If the refractive index of the fiber is 1.52 what is the smallest angle of incidencepossible when the light pipe is in air.n2=1.00n1=1.52θ1θ2= 90112 2n sin n sinθ= θ211nsin90(1.0)(1.0)sin 0.66n1.52θ= = =o141θ=Fiber OpticsFiber optics are used extensively in communications. Telephone, Internet, The high frequency of light (compared to microwaves) allows it to be switched rapidly and carry more information.3Dispersion• Dispersion is the separation of light with different colors due to the wavelength dependence of the index of refraction of a prism.Wavelength dependence of nFor most materialsn increases with decreasing wavelengthHighest in the blue regionLowest in the red regionDifferent colors are refracted by different angles in a prismDispersion of light by a prismExample A prism disperses white light into different colors.A 90 degree prism of crown glass refracts light normally incident on the long surface. Is violet light or red light refracted more.θ1=θn1n=1.000011 212sin sinsin==nnnsinnθθθθθ1θ2violet n1= 1.538 red n1= 1.516θSince n is greater for violet light than for red light Violet light is refracted moreExample A prism disperses white light into different colors.A 90 degree prism of crown glass refracts light normally incident on the long surface. For what value of θ gives the largest dispersion ∆θθ1=θn1n=1.000011 212sin sinsin==nnnsinnθθθθθ1θ2violet n1= 1.538 red n1= 1.516θviolet redarc sin(n sin ) arc sin(n sin )∆θ= θ − θ4Vary θn1n=1.0000θ1∆θθmax difference when θ2-> 90o for violetθ=40.556∆θ ~9.5 degreesThe large difference is because near 90o (Maximum) sin θ is quite insensitive to θat θ=40.556oθsinθ90o0123456789100 102030405060708090θ2 violet (degrees)∆θ (degrees)RainbowA rainbow is seen on a rainy day when the sun is to your back,low in the horizon (less than 42oabove the horizon)A second rainbow is often seen with the order of colorsreversed.The shape of the rainbow is due to parallel beam of sunlight lightreflected and refracted from raindrops at a special angle (rainbow angle of 40o-42o)The colors of the rainbow are due to dispersion of the light.Dispersion of light by a rain dropThree interfacesA) RefractionB) ReflectionC) RefractionA)B)C)Violet light is refracted morebut gives a smaller rainbow
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