All Problems Diffraction of Light
Problem 5.120
Making use of the result obtained in the foregoing problem, find the conditions defining the angular position of maxima of the first, the second, and the third order.
\(5.120 .\) The condition for a maximum leads to the transcendental equation \(\tan \alpha=\alpha,\) where \(\alpha=(\pi b / \lambda) \sin \theta .\) The solution of this equation (by means of plotting or selection) provides the following root values: \(\alpha_{1}=1.43 \pi, \alpha_{2}=2.46 \pi, \alpha_{3}=3.47 \pi .\) Hence \(b \sin \theta_{1}=\) \(=1.43 \lambda, b \sin \theta_{0}=2.46 \lambda, b \sin \theta_{3}=3.47 \lambda\)