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 whole course material, and it will be composed 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. Let’s translate it into the language of phases: How do we know, whether we are in a node or an antinode? where m is an integer The two waves at distances r 1 and r 2 : Constructive interference: The two sources oscillate in phase: at The result of interference will depend on phase difference, which does not depend on time!

3. The oscillations will be out of phase and the interference will be destructive if r 1 - r 2 = /2 or, r 1 - r 2 = - /2  or in general: How do we know, whether we are in a node or an antinode? 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 r 1 and r 2. Their difference for small angles  , small y/L

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

7. − intensity of either wave alone In general, the distribution of intensity on the screen: 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. Does this look any familiar? In the case when The intensity The intensity has a minimum of 0, maximum of 4S 0, and a mean value of 2S 0 – the same as for non-coherent sources (!) Electric field:

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

11. Composite wave: 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 Electric field:

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.html 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%2Bdiff raction%26start%3D160%26hl%3Den%26lr%3D%26sa%3DN http://vsg.quasihome.com/interf.htm http://www.ngsir.netfirms.com/englishhtm/Diffraction.htm http://www.walter-fendt.de/ph11e/interference.htm