Key Equations

Destructive interference for a single slit	$a\text{sin}\theta =m\lambda \text{for}m=\pm 1,\pm 2,\pm 3,...$
Half phase angle	$\beta =\frac{\varphi }{2}=\frac{\pi a\text{sin}\theta }{\lambda }$
Field amplitude in the diffraction pattern	$E=N\text{Δ}{E}_0\frac{\text{sin}\beta }{\beta }$
Intensity in the diffraction pattern	$I=I_0{\left(\frac{\text{sin}\beta }{\beta }\right)}^2$
Rayleigh criterion for circular apertures	$\theta =1.22\frac{\lambda }{D}$
Bragg equation	$m\lambda =2d\text{sin}\theta ,m=1,2,3...$