Chapter 37, Problem 6P

What If? Suppose light strikes a single slit of width a at an angle β from the perpendicular direction as shown in Figure P37.6. Show that Equation 37.1, the condition for destructive interference, must be modified to read

$\begin{array}{c}\sin {\theta }_{\text{dark}}=m\frac{\lambda }{a}-\sin \beta \\ m=\pm 1,\pm 2,\pm 3,\dots \end{array}$