CALC The intensity of light in the Fraunhofer diffraction
Chapter 36, Problem 36.58(choose chapter or problem)
The intensity of light in the Fraunhofer diffraction pattern of a single slit is
\(I=I_{0}\left(\frac{\sin \gamma}{\gamma}\right)^{2}\)
where
\(\gamma=\frac{\pi a \sin \theta}{\lambda}\)
(a) Show that the equation for the values of \(\gamma\) at which I is a maximum is \(\tan \gamma=\gamma\) (b) Determine the three smallest positive values of \(\gamma\) that are solutions of this equation. (Hint: You can use a trial-and-error procedure. Guess a value of \(\gamma\) and adjust your guess to bring \(\tan \gamma\) closer to \(\gamma\). A graphical solution of the equation is very helpful in locating the solutions approximately, to get good initial guesses.)
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