Draw normal lines bisecting the phasors they

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Unformatted text preview: φ/2) Don’t forget … The prelab is due at the beginning of lab !! Lecture 4, p 27 Supplementary Slides Lecture 4, p 28 Multi-Slit Interference We already saw (slide 4) that the positions of the principal maxima are independent of the number of slits. Here, we will use phasors to determine the intensity as a function of θ. y Incident wave (wavelength λ) S3 A1 θ d S2 At each principal maximum (d sinθ = mλ), the slits are all in phase, and the phasor diagram looks like this: A1 P S1 L A1 Atot = N A1 à༎ Itot = N2 I1 For other values of θ, the phasors are rotated, each by an angle φ with respect to its neighbors. Remember that φ/2π = δ/λ = d/λ sinθ. We can calculate Atot geometrically (next slide). Atot A1 φ A1 A1 φ Lecture 4, p 29 Multi-Slit Interference (2) The intensity for N equally spaced slits is found from phasor analysis. Draw normal lines bisecting the phasors. They intersect, defining R as shown: φ R R φ 2 φ 2 φ 2 φ 2 φ Substitute A1/2 N slits: R Nφ R A1 A1 φ = R sin ⇒ R = 2 2 2sin (φ / 2 ) Atot Atot Nφ = R sin ⇒ 2 2 Atot = A1 Itot Nφ 2 sin ( Nφ / 2 ) sin (φ / 2 ) ⎛ྎ sin(Nφ / 2) ⎞ྏ = I1 ⎜ྎ ⎟ྏ ⎝ྎ sin(φ / 2) ⎠ྏ 2 φ A1 Lecture 4, p 30 Single-slit Diffraction δa = a sinθ ≈ aθ To analyze diffraction, we treat it as interference of light from many sources (i.e., the Huygens wavelets that originate from each point in the slit opening). Model the single slit as M point sources with spacing between the sources of a/M. We will let M go to infinity on the next slide. θ a L The phase dif...
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This note was uploaded on 03/27/2014 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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