Template:Incident angle

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When a wave in incident at an angle [math]\theta [/math] we have the wavenumber in the [math]y[/math] direction is [math]k_y = \sin\theta k_0[/math] where [math]k_0[/math] is as defined previously (note that [math]k_y[/math] is imaginary).

This means that the potential is now of the form [math]\phi(x,y,z)=e^{k_y y}\phi(x,z)[/math] so that when we separate variables we obtain

[math] k^2 = k_x^2 + k_y^2 [/math]

where [math]k[/math] is the separation constant calculated without an incident angle.