A helium-neon laser,

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

Optics and Photonics, Ch Fraunhofer diffraction from apertures and gratings

Problem

A helium-neon laser, λ=632.8 nm\lambda = 632.8\ \text{nm}, illuminates a slit of width b=0.050 mmb = 0.050\ \text{mm}, and the diffraction pattern is viewed on a screen L=2.0 mL = 2.0\ \text{m} away (checked to be in the Fraunhofer regime). The single-slit pattern is a phasor chain of fixed arc length E0E_0, bent smoothly through a total angle 2β2\beta as θ\theta moves off axis, β=πbsin⁡θ/λ\beta = \pi b\sin\theta/\lambda. Take β2=4.493 rad\beta_2 = 4.493\ \text{rad} as given for the angle of the first secondary maximum (it solves tan⁡β=β\tan\beta=\beta). ((a)) Describe the shape the phasor chain has taken at the first minimum, in terms of its total turning angle and its resultant, and find the angle θ1\theta_1 and the position y1y_1 on the screen where it occurs. ((b)) Describe the phasor chain's shape at the first secondary maximum, and find θ2\theta_2 and y2y_2 on the screen.

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