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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 N1 zeros and
N2 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 NSlit 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 Nslit 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.
 Spring '08
 Staff
 Quantum Physics, Diffraction

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