228s12-l07 - Physics 228 Today More...

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Physics 228 Today: More diffraction/interference Website: Sakai 01:750:228 or www.physics.rutgers.edu/ugrad/228 Summer research internships may still be possible - see: http://www.youtube.com/watch?v=5lcSGNDRonw&feature=youtu.be or http://see.orau.org / Mastering Physics grades: a bunch of people are not getting grades either because - they registered twice and the 0 grades overwrite the non-0 grades. This changes randomly week to week because of the order I upload the two classes. Or because they registered but did not give their RU 9-digit student ID number, and gradebook does not recognize them on upload. If you have either problem and cannot fix it, tell me. Thursday, February 9, 2012
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Single Slit Diffraction Intensity Consider in the slit all the electric fields from each little point / strip in the slit to be aligned / in phase. At the central point O, the electric fields are all basically still aligned; the path length differences are small compared to a wavelength. Recall: (1+ δ ) p 1 + p δ + ... Thus: Δ x = (a 2 /4+R 2 )-R Δ x = R (1+a 2 /8R 2 + ...) - R Δ x = a 2 /8R + ... In out demos, a 0.3 mm, R 10 m, Δ x/ λ 1 nm / 600 nm << 1 Thursday, February 9, 2012
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What happens as you move away from point O? By the first minimum, the upper half of the slit has a path length difference of λ /2 from the lower half, so there is a total difference of λ over the entire slit. Consider being at some point a short distance below O, at an angle θ below the horizontal from the center of the slit. The path length difference between rays from the top to the bottom of the slit is: a sin θ θ a The phase difference corresponding to this path length difference is: β = 2 π Δ x / λ = 2 π a sin θ / λ θ Thursday, February 9, 2012
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What happens as you move away from point O? You add vectors but putting them tail to head, and the sum goes from the initial tail to the final head. Divide the slit in small sections. Each has slightly different path length so generates electric fields at slightly different phase angles. Graph them and put them tail to head. E p is the sum of all of them. The total phase difference, and thus total angle between the first and last section of the slit, is: β = 2 π Δ x / λ = 2 π a sin θ / λ .
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