Changes

== Interference ==

== Interference ==

[[Image:06 Spherical Propogation.png|thumb|Each point on the wavefront generates spherical wavelets.]]

[[Image:06 Spherical Propogation.png|thumb|Each point on the wavefront generates spherical wavelets. Note that the waveform is not uniform.]]

The propogating wavefront generates spherical wavelets as it propogates. What we want to know is what the wave at the initial point <math> f(x,y,0,t) </math> will look like at <math>f(x,y,D,t)</math>. To do this, we can integrate over the product of this equation times a propogator g.

The propogating wavefront generates spherical wavelets as it propogates. What we want to know is what the wave at the initial point <math> f(x,y,0,t) </math> will look like at <math>f(x,y,D,t)</math>. To do this, we can integrate over the product of this equation times a propogator g.

<math> g( x_i, t_i, x_f, t_f)\,</math>

<math> g( x_i, t_i, x_f, t_f)\,</math>

Because the propogator is actually in terms of the differences between the x and t values, we will write the difference between the x-vectors as <math>\Delta x</math> and the difference between the times as <math>\Delta t</math>.

Because the propogator is actually in terms of the <i>differences</i> between the x and t values, we will write the difference between the x-vectors as <math>\Delta x</math> and the difference between the times as <math>\Delta t</math>.

The integral is therefore

The integral is therefore