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Unformatted text preview: of λ, d and N). 0 θmin λ/d θ Lecture 4, p 6 Solution
In an N-slit interference pattern, at what angle θmin does the
intensity first go to zero? (In terms of λ, d and N). 0 λ/d θmin θ 2 ⎛ྎ sin( Nφ / 2) ⎞ྏ has a zero when the numerator is zero. That is, φmin = 2π/N.
I N = I1 ⎜ྎ
sin(φ / 2) ⎠ྏ Exception: When the denominator is also zero.
That’s why there are only N-1 zeros. But φmin = 2π(d sinθmin)/λ ≈ 2πd θmin/λ = 2π/N. Therefore, θmin ≈ λ/Nd. As the number of illuminated slits increases, the peak widths decrease!
General feature: Wider slit features à༎ narrower patterns
Narrower slit features à༎ wider patterns.... Lecture 4, p 7 Note:The simple calculations we have done only hold in
the “far-field” (a.k.a. “Fraunhofer” limit),
where L >> d2/λ.
Intermediate cases (“Fresnel diffraction”) can be much
more complex… Interference Gratings
Examples around us.
CD disk – grooves spaced by ~wavelength of visible light. The color of s...
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