Chapter 27, Problem 14P

Coherent light rays of wavelength λ strike a pair of slits separated by distance d at an angle θ₁, with respect to the normal to the plane containing the slits as shown in Figure P27.14. The rays leaving the slits make an angle θ₂ with respect to the normal, and an interference maximum is formed by those rays on a screen that is a great distance from the slits. Show that the angle θ₂ is given by

${\theta }_2={\sin }^{-1}\left(\sin {\theta }_1-\frac{m\lambda }{d}\right)$

where m is an integer.