# feb06c - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Chapter 2 Assorted subproblems For the first example of dividing into unlike subproblems, we estimate the spacing between pits on a CD ROM. Then we estimate the amount of oil that the United States imports annually. 2.1 Pits on a CDROM Q: What is the spacing between the pits on a CDROM? The pits (indentations) are the memory elements, each pit storing one bit of information. A quick estimate comes from turning over a CDROM and enjoying the brilliant colors. The colors arise because the arrangement of pits diffracts visible light by a significant angle, and the angle depends strongly on the wavelength (or color). So the pits are spaced comparably to the wavelength of light, say about 1 µ m. A second estimate might come from knowing a bit about the laser in a CD player or in a CDROM drive. It is a near-infrared laser, so its wavelength – which will be comparable to the pit size and spacing – is slightly longer than visible-light wavelengths. Since visible- light wavelengths range from 350 to 700 nm or from . 4 to . 8 µ m, a reasonable estimate for...
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feb06c - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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