where is the phase between adjacent slits 0 d 2d

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Unformatted text preview: the principal maxima occur at φ = 0, ±2π, ±4π, ... where φ is the phase between adjacent slits. θ = 0, ±λ/d, ±2λ/d, ... The intensity at the peak of a principal maximum goes as N2. 3 slits: Atot = 3A1 ⇒ Itot = 9I1. N slits: IN = N2I1. Between two principal maxima there are N-1 zeros and N-2 secondary maxima ⇒ The peak width ∝ 1/N. The total power in a principal maximum is proportional to N2(1/N) = N. Lecture 4, p 4 N-Slit Interference The Intensity for N equally spaced slits is given by: ⎛ྎ sin(Nφ / 2) ⎞ྏ IN = I1 ⎜ྎ ⎟ྏ sin(φ / 2) ⎠ྏ ⎝ྎ 2 * y Derivation (using phasors) is in the supplementary slides. θ As usual, to determine the pattern at the screen, we need to relate φ to θ or y = L tanθ: φ δ d sinθ dθ == ≈ 2π λ λ λ and θ ≈ d y L φ is the phase difference between adjacent slits. L You will not be able to use the small angle approximations unless d >> λ. * Your calculator can probably graph this. Give it a try. Lecture 4, p 5 Example Problem In an N-slit interference pattern, at what angle θmin does the intensity first go to zero? (In terms...
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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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