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Introduction To Reflection And Refraction Essay

5216 words - 21 pages

1.1 IntroductionThis "book" is not intended to be a vast, definitive treatment of everything that is knownabout geometric optics. It covers, rather, the geometric optics of first-year students,whom it will either help or confuse yet further, though I hope the former. The part ofgeometric optics that often causes the most difficulty, particularly in getting the rightanswer for homework or examination problems, is the vexing matter of sign conventionsin lens and mirror calculations. It seems that no matter how hard we try, we always getthe sign wrong! This aspect will be dealt with in Chapter 2. The present chapter dealswith simpler matters, namely reflection and refraction at a plane surface, except for abrief foray into the geometry of the rainbow. The rainbow, of course, involves refractionby a spherical drop. For the calculation of the radius of the bow, only Snell's law isneeded, but some knowledge of physical optics will be needed for a fuller understandingof some of the material in section 1.7, which is a little more demanding than the rest ofthe chapter.1.2 Reflection at a Plane SurfaceThe law of reflection of light is merely that the angle of reflection r is equal to the angleof incidence r. There is really very little that can be said about this, but I'll try and saywhat little need be said.i. It is customary to measure the angles of incidence and reflection from the normal tothe reflecting surface rather than from the surface itself.i rFIGURE I.12ii. Some curmudgeonly professors may ask for the lawS of reflection, and will give youonly half marks if you neglect to add that the incident ray, the reflected ray and thenormal are coplanar.iii. A plane mirror forms a virtual image of a real object:or a real image of a virtual object:FIGURE I.2• O I °FIGURE I.3• I O °3iv. It is usually said that the image is as far behind the mirror as the object is in front ofit. In the case of a virtual object (i.e. light converging on the mirror, presumably fromsome large lens somewhere to the left) you'd have to say that the image is as far in frontof the mirror as the object is behind it!v. If the mirror were to move at speed v away from a real object, the virtual imagewould move at speed 2v. I'll leave you to think about what happens in the case of avirtual object.vi. If the mirror were to rotate through an angle θ (or were to rotate at an angular speedω), the reflected ray would rotate through an angle 2θ (or at an angular speed 2ω).vii. Only smooth, shiny surfaces reflect light as described above. Most surfaces, suchas paper, have minute irregularities on them, which results in light being scattered inmany directions. Various equations have been proposed to describe this sort ofscattering. If the reflecting surface looks equally bright when viewed from all directions,the surface is said to be a perfectly diffusing Lambert's law surface. Reflectionaccording to the r = i law of reflection, with the incident ray,...

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