Physic Labs

Problem 3

Monochromatic light of wavelength λ\lambda is incident normally on a single slit of width bb. A parallel screen is at distance LL, with L≫bL\gg b so Fraunhofer diffraction applies. Intensity is observed at a small angle θ\theta from the normal through the slit centre; ignore the finite screen size and other edge effects. (a) Divide the aperture into elements and state the condition for cancellation of their amplitudes. (b) Find the angle θ1\theta_1 of the first dark minimum. (c) Derive its screen displacement y1y_1 and explain why this is a dark fringe rather than a maximum.
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θ1≃λb,y1=Ltan⁡θ1\theta_1\simeq\frac{\lambda}{b},\quad y_1=L\tan\theta_1
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For small angles, sin⁡θ≃tan⁡θ≃θ\sin\theta\simeq\tan\theta\simeq\theta, relating the minimum angle to screen geometry. The stated Fraunhofer and small-angle approximations are used.