class26lecnotes - Class 26, Friday, March 12, 2010...

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Class 26, Friday, March 12, 2010 Reading:~/. l ).3" 3 3:'''; PllE----- Magical Black Box How can we get all rays to meet at one point, P ,? This question could be reformulated in the following way: How can we make all "least times" for light to travel from P to Po the same? In other words: ~=tl=~=t3='" Is this possible with a straight piece of glass? A simple glance at the figure above shows that this is not possible. The paths that light takes through the glass differ, and so do the times. We would need to artificially shorten the time spent on the longer paths. The magical device that takes care of these problems is the lens. A convex lens artificially shortens the time that light spends going through the longest paths (around the extremities of the glass. There the lens is thinnest, so light only travels through the slower medium a short distance, thus making up for traveling overall a longer distance. A convex lens also lengthens the paths around the optical axis, thus delaying the travel time for light through those regions, which otherwise are geometrically shorter. / The oldest known lens was excavated at tJ;iiimJ and dates back to 640 BC The oldest written record about the usage of lenses goes back to the ancient Greeks (ca. 400 Be). From here to actually making lenses usable, it takes sufficiently accurate grinding technologies. These were not available until much later: Spectacles were in wide circulation in the early 1600. and the telescope was invented. in 1668. Making and using lenses, however, does not tell us much about the underpinning theory. The first elaborate optical treatise goes back to the Arab physicist Alhazen (ca. 900 AD) . .2b.1
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,)). How do we shape the lens so that it does what we want it to do? We will understand how lenses work in a series of steps. 1. Single Refracting Surface. We want a surface so that: 1) The time tpAP,=tPBP' for all points A on this surface! 2) All rays coming from P are bent toward P'. Such a surface turns out to be hard to make. Within certain approximations, however. matters can be simplified. For example, if we only consider rays originating close to the optical axis, the surface that fulfills our requirements turns out to be spherical. Such rays are called paraxial rays. In reality. we can never eliminate the rays that are not close to the axis. They cause trouble for optical instruments, and we will look at these issues later.
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This note was uploaded on 03/16/2010 for the course PHYS 6B taught by Professor Graham during the Winter '08 term at University of California, Santa Cruz.

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class26lecnotes - Class 26, Friday, March 12, 2010...

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