Class Note for PH 106 at UA-Generl Physics WCalc II (2)
Class Note for PH 106 at UA-Generl Physics WCalc II (2)
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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 22 views.
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Date Created: 02/06/15
PH 106 Dr T Mewes Chapter 35 Light and the laws of geometric optics The nature of light There has been quite some controversy about the nature of light today we regard light to have a dual nature Light exhibits the characteristics of a wave see for example Chapter 34 but it also has the characteristics of a particle see chapter 40 The particle picture was used by Einstein in 1905 he received the Nobel Prize for this work in 1921 to explain the so called photoelectric effect According to Einstein the energy of the light particles photons is proportional to the frequency f of the electromagnetic wave Eh f 1 where the proportionality constant h 663X19 34 Js is called Planck s constant Speed of light The speed oflight cis 2979x1033 2 S which is about 67gtlt10E miles per hour The fact that light travels at such a high speed made it dif cult to measure the speed of light In 1675 Ole Roemer made the first successful measurement of the speed of light he observed that Jupiters moon lo time complete one orbit about 425 hours changed slightly when the earth and Jupiter were moving towards each other compared to times when Jupiter and earth were moving away from each other The significance of those measurements was that they established a finite speed of light In 1849 Hippolyte Fizeau developed a method to measure the speed oflight on earth liahl source W5 W3 mlaling mu m AX39L By knowing the distance between the mirror and the wheel the number of teeth in the wheel and its angular speed forwhich the observer can see the light back re ected he was able to calculate the speed of light 14 PH 106 Dr T Mewes Ray approximation in geometric optics The propagation of light can be studied using geometric optics which assumes that light travels in a fixed direction in a straight line when it passes trough a uniform medium Light changes its direction when it meets the surface of a different medium or when the medium it travels in is nonuniform The rays of an electromagnetic wave light are straight lines perpendicular to the wave fronts as shown below Rays Wavefronts The ray approximation is valid as long as the dimensions of the objects involved are large compared to the wavelength of the light When the dimension an object is comparable with the wavelength of the light the waves will spread out and one will observe diffraction see chapter 37 Reflection When light encounters the surface ofanother medium part of the light will be reflected If the surface is smooth we call this specular reflection whereas a rough surface with surface variations comparable or larger than the wavelength leads to diffuse reflection The term reflection is often used having specular reflection in mind we will do so in the following Normal Incident Re ected ray E ray Medium 1 Medium 2 24 PH 106 Dr T Mewes Law of reflection 191 91 3 The angle of reflection equals the angle of incidence Refraction When light encounters the surface ofanother medium part ofthe light will enterthe other medium we call this refraction Normal Incident Re ected ray ray Medium 1 Medium 2 I Refracted ray The angle of refraction 62 depends on the angle of incidence 61 and the properties of the two media as follows ihi 39z V2 lt4 1 here v1 is the speed of light in medium 1 and v2 is the speed of light in medium 2 For air one has vl m 3x108 ms whereas glass for example has a speed of light of v2 m 2gtlt108 ms This leads to the de nition of the index of refraction or refractive index n for a medium W sp e dbfljghtm Vfci cuum c 4 5 Speed 0f light39zn medwm v V th this one can rewrite equation 4 for two media with refractive indices n1 and n2 39Sih z L2 i 1 6 sin l 1 n2 0 112 which is known as Snell s law of refraction sin19 2 71139 Isint91 6 34 PH 106 Dr T Mewes The index of refraction can also be used to relate the wavelengths in the different media First we note that the frequency of an electromagnetic wave does not change as one goes from one medium to the other ie f1 f2 f Now we can use that V1 11f and v2 M 8 which gives L2 1 9 or 32 11 quot2 10 12 V2 711 C 711 From this equation we see that the wavelength in a medium n2gt1 is always smaller than the wavelength in vacuum n11 Dispersion The index of refraction n typically depends on the wavelength of the light this is called dispersion This leads to the formation ofa rainbow Total internal reflection Light coming from a medium with a higher index of refraction toward a medium with a lower index of refraction can lead to an effect called total internal reflection When this happens the angle of the refracted light 62 90 ie the refracted ray travels along the interface of the two media The incident angle for which this happens is called the critical angle 6C for angles greater than this the light is entirely re ected back into the rst medium From Snell s law we have forthe critical angle nZsin90 n1sint9c 11 Or sint9C quot 2 1139 for n1gtn2 quotI This effect is used in optical fibers to get light from one point to another with minimal losses 44