Chapter 35The Ray Approximation of Light in Geometric OpticsReflection of LightLaw of ReflectionRetroreflectionOne more example problemRefraction of LightSnell’s Law of RefractionReflection and RefractionSome Indices of RefractionFrequency Between MediaVariation of Index of Refraction with WavelengthDispersionPrismThe Rainbow, a Nature’s show of dispersionDouble RainbowTotal Internal ReflectionDiamond or glass?Fiber OpticsFiber opticsFiber Optics, cont.Construction of an Optical FiberChapter 35The Laws of Geometric OpticsThe Ray Approximation of Light in Geometric Optics Geometric optics studies the propagation of light. Light travels in a straight-line path in a uniform medium. Light changes its direction when it meets the interface of two media. Here reflection and refraction take place. Propagation of light in non-uniform medium is not discussed here. The ray approximation is used to represent beams of light. Each ray is represented as a line. The rays are straight lines perpendicular to the wave frontsThe path of light is reversible.Reflection of LightReflection: a ray of light, the incident ray, changes its direction at the interface of two media, and travels back in the same medium of the incident ray. Two types of reflection:Specular reflection: reflection from a smooth surface. For parallel incidence, the reflected rays are parallel to each other. Diffuse reflection: reflection from a rough surface. Reflected rays travel in a variety of directions even for parallel incidence.We will only discuss specular reflections here.Specular reflectionDiffuse reflectionMedium 1Medium 2Medium 2Medium 1Law of ReflectionThe incident angle and the reflection angle.Incident angle: the angle ( in the diagram) the incident ray makes with the normal of the interface at which the reflection takes place.Reflection angle: the angle ( in the diagram) the reflected ray makes with the normal of the interface at which the reflection takes place.The Law of reflection:The incident ray, the reflected ray and the normal are all in one plane.1'q1q1 1'q q=1 1'q q=RetroreflectionRetroreflection: reflected light travels in parallel but opposite in direction to the incident light. Can be achieved by two plane mirrors with an angle of 90o between them.Applications includeMeasuring the distance to the MoonAutomobile taillightsTraffic signsqq2pq-2pq-2pq-One more example problemThe distance of a lightbulb from a large plane mirror is twice the distance of a person from the same mirror. Light from the lightbulb reaches the person by two paths. It travels to the mirror at an angle of incidence θ and reflects from the mirror to the person. It also travels directly to the person without reflecting off the mirror. The total distance traveled by the light in the first case is twice the distance traveled by the light in the second case. Find the angle θ.Refraction of LightRefraction: When light enters from one medium to the second, it changes its direction in the second medium. The angle the refracted light makes with the normal ( in the diagram) is called the angle of refraction. The incident ray, the reflected ray, the refracted ray, and the normal all lie in the same plane.The reason for this bent is because light travels at different speeds in different medium: Here is the speed of light in medium 1, is the speed of light in medium 2.2qMedium 1Medium 21 12 2sin vsin vqq=2v1vSnell’s Law of RefractionThe index of refraction:Because the speed of light in any material is less than its speed in vacuum, index of refractionFor a vacuum, n = 1For air n = 1 is a very good approximation.For other media, n > 1Snell’s Law of refractionspeed of light in vacuumspeed of light in mediumcnv� =1 1 2 2n sin n sinq q=1n �1airn �1 52glassn .�Reflection and Refraction2q1'q1q2q1qSome Indices of RefractionFrequency Between MediaWhen light travels from one medium to another, its frequency (and color) does not change (this comes from energy conservation)Both the speed and the wavelength do changeFrom:One has:121 1 21 1 2 22 2 1 or cncnv n, n nv nll ll= = = =1 2 and v f , f fTll= = =Also from: and cv f , nvl= �We know that index of refraction is a (weak) function of frequency (color). Different colors of light bent differently when refracted.Variation of Index of Refraction with WavelengthThe index of refraction for a material generally decreases with increasing wavelengthViolet light bends more than red light when passing into a refracting materialDispersionFor a given material, the index of refraction varies with the wavelength of the light passing through the materialThis dependence of n on (in vacuum) is called dispersionSnell’s law indicates light of different wavelengths is bent at different angles when incident on a refracting materiallPrismA ray of single-wavelength light incident on the prism will emerge at angle from its original direction of travel is called the angle of deviation is the apex angleThe angle can be expressed as a function of the incident angle and the apex angle. When a ray of white light (many colors) enters a prism, the color components are separated out into a spectrum:Violet deviates the mostRed deviates the leastThe remaining colors are in between.The Rainbow, a Nature’s show of dispersionSun light refracted/reflected by rain drops has its color components separated into color spectrum. The angle between the white light and the most intense violet ray is 40°The angle between the white light and the most intense red ray is 42°Double RainbowThe secondary rainbow is fainter than the primaryThe colors are reversedThe secondary rainbow arises from light that makes two reflections from the interior surface before exiting the raindropHigher-order rainbows are possible, but their intensity is lowTotal Internal Reflection When light travels from a medium with larger index of refraction to a medium with smaller n, as in the diagram n1 > n2. The refracted angle is larger than the incident angle. As the incident angle increases to the point that the refracted angle is 90o, this incident angle is called the critical angle θc. Beyond it, there is no refraction. All light is reflected back and this phenomenon called total internal reflection.From Snell’s Law: 1 2cn sin nq =When medium 2 is air:
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