Why is the phase difference -k'r for diffracted waves in diffraction?

[PhysicsGirl90]

Hello everybody,

I'm having some trouble comprehending the following image. I am supposed to be able to deduce from the figure that the total difference in phase angle is (k-k')r. To begin with, I do not understand why for the diffracted wave the difference in phase angle is -k'*r while for the incomming wave it is just k*r. Where does the minus sign come from?

Thanks in advance...

 

[BruceW]

Hmm. The picture is a geometric way of showing what is going on and the equation is a way to show it as a vector relation.

So you need to think of the picture in terms of vectors, keeping in mind the definition of the dot product, then you'll see where the minus comes from.

 

[PhysicsGirl90]

Thanks Bruce, with your hints about the vectors I finally understood where everything comes from.

 

[BruceW]

That's good. You did the work, I just gave you a kick in the right direction ;)