1Refraction, the Snell law Light 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:irθθ=Incident lightNormal of the interfaceReflected lightθ1and θ2are both with respect to the normal of the interface.The parameters n1and n2are call the index of medium 1 and 2 respectively.2211sininθθnsn=Medium 1Medium 2θ1θ22Refraction, the index of refraction of a medium Light 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:from222211=⋅=⋅=θθθθ50811099110003882.s/m.s/m.vcn =××=≡o....n,nnsn74953sin331sin0001(water)331(air)1sinin:from1o1212211=⋅=⋅===θθθθ4Snell’s Law examplesθ1θ2θ3If θ1 is 40 degrees, what is θ2 and θ3?oooo.....n,.nnsn....n,.nnsn767sin111025sin432111432sinin:fromagain025sin43240sin601432601sinin:from3332332222212211=⋅=⋅====⋅=⋅===θθθθθθθθ5total 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 reflectionhappens.211212sinininnnnnssc===θθθ6Total internal reflectionTotal internal reflection only happens when light travels from amedium with larger index of refraction to a medium with smaller index of refraction. The critical angle θccalculated below. Beyond it, total internal reflection happens.12211212sininin nn,nnnnssc>===θθθExample: light travel from glass to air, what is the critical angle when total internal reflection happens?oc....n,.nnsn540sin90001sin541(air)001(glass)541sinin:fromoc212211=⋅=⋅===θθθθ7ExampleYou 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:fromoc212211=⋅=⋅===θθθθoc....n,.nnsn424sin90001sin422(air)001(diamond)422sinin:fromoc212211=⋅=⋅===θθθθoc....n,.nnsn434sin90001sin771(air)001(sapphire)771sinin:fromoc212211=⋅=⋅===θθθθdiamondglass8Fiber 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./.,..nn8335570sin1601in001cos)90sin(sinin6151sin501sin601sin90sin:from21110co2c1==−=⋅=−====⋅⋅=⋅αθαθθβαθθθ9Wavelength of light in different media Color 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=0λfnnvcfmλλ===0nm0λλ=so, becomes shorter10Wavelength of light in different media Can you prove: 2211λλnn=2211221121orandso:haveweλλλλλλλnnncncncfncfTvff=======11Dispersion and prisms The 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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