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The final will be given on Wednesday, March 18th, from 11:30 AM to 2:30 PM , in Warren 2001.

The final will be given on Wednesday, March 18th, from 11:30 AM to 2:30 PM , in Warren 2001. Your student I.D. is required to take it. The final will be a closed-book exam and cover the whole course material, and it will be composed of multiple choice problems, just like the quizzes.

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The final will be given on Wednesday, March 18th, from 11:30 AM to 2:30 PM , in Warren 2001.

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  1. The final will be given on Wednesday, March 18th, from 11:30 AM to 2:30 PM, in Warren 2001. • Your student I.D. is required to take it. • The final will be a closed-book exam and cover the wholecourse material, and it will becomposed of multiple choice problems, just like the quizzes. • There will be ~24 problems, 2-3 per each week of the class. About a half of the problems will be conceptual. • You should bring a Scantron form with you. • You may use a calculator (but not a laptop) during the final. • You may also bring a single 8 1/2” x 11”sheet of paper of formulae and notes handwritten on the both sides. (Printed cheat-sheets are not allowed!) • You may wish to bring some blank scratch paper as well.

  2. How do we know, whether we are in a node or an antinode? Let’s translate it into the language of phases: The two sources oscillate in phase: at The two waves at distances r1 and r2: The result of interference will depend on phase difference, which does not depend on time! Constructive interference: where m is an integer

  3. How do we know, whether we are in a node or an antinode? The oscillations will be out of phase and the interference will be destructive if r1 - r2 = l/2 or, r1 - r2 = - l/2, or in general: where m is an integer number The phase difference:

  4. Can we see any interference without a laser?

  5. Some math: the slits are two coherent sources. The distances to the observation point are r1 and r2. Their difference for small anglesq, small y/L

  6. Approximation used: for small Constructive (a bright strip) Destructive (a dark strip)

  7. In general, the distribution of intensity on the screen: − intensity of either wave alone Bright and dark fringes:

  8. In the case when The intensity Positions of the bright and dark fringes (maxima and minima of interference) The distance between the fringes:

  9. In the case when The intensity The intensity has a minimum of 0, maximum of 4S0, and a mean value of 2S0 – the same as for non-coherent sources (!) Electric field: Does this look any familiar?

  10. Composite wave: The intensity Electric field: Looks very much like a standing wave with What are the differences?

  11. Composite wave: Electric field: Unlike the standing waves on a string:in the interference, the pattern of bright and dark fringes is created along the y-axis, whereas the wave itself propagates along the x-axis;unlike the distance between regular nodes and antinodes the distance between the dark and bright fringes is not 1/2 of the wavelength, but rather

  12. What happens if we have got 3 or more slits? The condition for constructive interference (bright fringes) does not change form the 2-slit apparatus: or But the condition for destructive interference for N slits changes to: where m is an integer but not an integer multiple of N How does the resulting interference pattern look like?

  13. The maxima, bright fringes, become brighter and narrower as the number of slits increases. Most of the interference pattern becomes dark. For N slits: Maximal intensity in bright fringes: Average intensity:

  14. http://id.mind.net/~zona/mstm/physics/waves/interference/twoSource/TwoSourceInterference1.htmlhttp://id.mind.net/~zona/mstm/physics/waves/interference/twoSource/TwoSourceInterference1.html http://www.ngsir.netfirms.com/englishhtm/Diffraction.htm http://www.spa.umn.edu/groups/demo/waves/3B5010.html&h=240&w=320&sz=9&tbnid=GWEiiWBVHAcJ:&tbnh=84&tbnw=112&start=163&prev=/images%3Fq%3Dslit%2Bdiffraction%26start%3D160%26hl%3Den%26lr%3D%26sa%3DN http://vsg.quasihome.com/interf.htm http://www.walter-fendt.de/ph11e/interference.htm

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