All Problems

Diffraction of Light

Problem 5.102

A plane monochromatic light wave with intensity I0I_{0} falls normally on the surfaces of the opaque screens shown in Fig. 5.20. Find the intensity of light II at a point PP (a) located behind the corner points of screens 1−31-3 and behind the edge of half-plane 4 ; (b) for which the rounded-off edge of screens 5−85-8 coincides with the boundary of the first Fresnel zone. Derive the general formula describing the results obtained for screens 1−4;1-4 ; the 1441/3\frac{14}{4^{1 / 3}} same, for screens 5−85-8.

Reveal Answer
5.102. (a) I1≈ϑ/16I0,I2=1/4I0,I3=1/16I0,I4=I2,I≈I_{1} \approx \vartheta /{16} I_{0}, \quad I_{2}=1 / 4 I_{0}, I_{3}=1 /_{16} I_{0}, \quad I_{4}=I_{2}, \quad I \approx ≈(1−φ/2π)2I0;\approx(1-\varphi / 2 \pi)^{2} I_{0} ; (b) I5≈25/16I0,I6≈9/4I0,I7≈4ρ/16I0,I8=I_{5} \approx{ }^{25} /_{16} I_{0}, I_{6} \approx{ }^{9} / 4 I_{0}, I_{7} \approx{ }^{4} \rho /{16} I_{0}, \quad I_{8}= =I6,I≈(1+φ/2π)2I0.=I_{6}, I \approx(1+\varphi / 2 \pi)^{2} I_{0} . Here φ\varphi is the angle covered by the screen.
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