Refraction, the Snell lawRefraction, the index of refraction of a mediumSnell’s Law examplesSlide 4total internal reflectionTotal internal reflectionExampleFiber opticsWavelength of light in different mediaSlide 10Dispersion and prisms1Refraction, the Snell lawLight in geometric optics is discussed in rays and represented by a straight line with an arrow indicating the propagation direction.Light propagates in straight lines in homogenous medium. Light reflects on interface of two media, following the law of reflection:Light also refracts on the interface of two media, following Snell’s law of refraction:irIncident lightNormal of the interfaceReflected lightθ1 and θ2 are both with respect to the normal of the interface.The parameters n1 and n2 are call the index of medium 1 and 2 respectively.2211sininnsn Medium 1Medium 2θ1θ22Refraction, the index of refraction of a mediumLight travels with the speed of light c in vacuum with c = 3.00×108 m/sec.Light travels with a speed v in a transparent medium with v is always smaller than the c.The ratio of c to v is called the index of the refraction n of that medium and is weak function the light frequency. We will get to the frequency dependence part later.And it is this light speed difference in two different media that makes light a turn at the interface of the two media. Have you ever driven a tractor on belts or a tank? You turn to the direction by slowing that side of the belt down.vcn So light travels almost at the speed of light c in air. But light moves in diamond at about 40% of the speed of light c in vacuum. This is why diamond is so pricey. (you believe me here?)3Snell’s Law examplesθ1θ2If θ1 is 60 degrees, what is θ2 ?air 1water 2θ1θ2If θ2 is 35 degrees, what is θ1 ?oo...nsn035sin508160sin0001sinin:from22221150811099110003882.s/m.s/m.vcn o....n,nnsn74953sin331sin0001(water)331(air)1sinin:from1o12122114Snell’s Law examplesθ1θ2θ3If θ1 is 40 degrees, what is θ2 and θ3?oooo.....n,.nnsn....n,.nnsn767sin111025sin432111432sinin:fromagain025sin43240sin601432601sinin:from33323322222122115total internal reflectionθ1θ2θ3air 1water 2θ2θ1When θ2 is 30 degrees, θ1 is 41.7 degrees. When θ2 is 40 degrees, θ1 is 58.7 degrees. When θ2 is 48.75 degrees, θ1 is 90 degrees. When θ2 is 60 degrees, this is a refection problem. So θ2 is 48.75 degree, comes from Is called the critical angle θc . Beyond it, total internal reflection happens.211212sinininnnnnssc6Total internal reflectionTotal internal reflection only happens when light travels from a medium with larger index of refraction to a medium with smaller index of refraction. The critical angle θc calculated below. Beyond it, total internal reflection happens.12211212sininin nn,nnnnsscExample: light travel from glass to air, what is the critical angle when total internal reflection happens?oc....n,.nnsn540sin90001sin541(air)001(glass)541sinin:fromoc2122117ExampleYou are cutting a sapphire to make it as brilliant as possible. Find the critical angle for the sapphire in air. The index of refraction of a sapphire is 1.77.What would be the cut angle for diamond? And for glass?oc....n,.nnsn540sin90001sin541(air)001(glass)541sinin:fromoc212211oc....n,.nnsn424sin90001sin422(air)001(diamond)422sinin:fromoc212211oc....n,.nnsn434sin90001sin771(air)001(sapphire)771sinin:fromoc212211diamondglass8Fiber opticsWhat is the maximum angle α that results in total internal reflection inside the fiber optic cable? This angle is usually called the launching angle in fiber optics. occcoc...s.nnnsn./.,..nn83355 70sin1601in001cos)90sin(sinin6151sin501sin6 01sin90sin:from21110co2c19Wavelength of light in different mediaColor is often associated with wavelength. It is actually defined by the electromagnetic wave’s frequency. In vacuum, these two values are connected with the speed of light c in vacuum.When light travels in a medium with index of refraction n, the color and frequency keeps the same. Its wavelength changes as:Frequencywavelengthcf 0fnnvcfm0nm0so, becomes shorter10Wavelength of light in different mediaCan you prove: 2211nn 2211221121orandso:havewennncncncfncfTvff11Dispersion and prismsThe index of refraction is a weak function of wavelength that causes light to separate into its various wavelengths when it is refracted. This is the physics base for the rainbow.Each rain dropQuestion: if the incoming light is from a red laser, what color(s) do you see when the light exits the
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