Wave-partical duality and Huygens–Fresnel principle

[howaboutthis]

Hi all!

Couple days ago my friend asked me about the following. He said:

Consider a well-known problem in which light propagates through an opening in a plane opaque screen. As always, we consider linear dimensions of the opening to be large compearing to the wavelength and small comparing to the distances of A and P from the screen. According to Huygens, every point of the wave-front may be considered as a center of a secondary disturbance which gives rise to spherical wavelets and the wave-front at any later instant may be regarded as the envelop of these wavelets. Together with Fresnel assumption about the mutual interference of the secondary wavelets and with his zone-construction also, Huygens–Fresnel principle leads to a conclusion that the intension of the light at P depends on how much Fresnel zones are opened. Ok, this is what wave theory says. How about photons? In fact, if we consider a point B on the wave-front, Huygens–Fresnel principle says that a photon with a certain momentum p when reaches to this point should change the direction from AB to BP (if he whants to arrive to P). But this contradicts with the law of conservation of momentum! So there are only two kind of photons that could start at point A and go to P: one in a straight line AP and another in AM-MP direction (interacting with the screen at M).

[PLAIN]http://img685.imageshack.us/img685/2886/dualism.png[/CENTER]

I have explained it to him in this way. The meaning of the quantum theory of light is NOT that we consider the light as being a gas of particles with energy $$\hbar \omega$$ and momentum $$\hbar \mathbf{k}$$, but rather that an exchange of energy and momentum between light and matter is done by small pieces -- quanta. In this particular problem we calculate the propagation of the light as it was a wave (Huygens–Fresnel principle in rigorous Kirchhoff formulation allows us to do this almost preсisely), but when the light reaches the point P, we interpret the intension of the light as the probability of finding a photon at this point.

Am I right?

Thanks.​

 

[howaboutthis]

Is this such a hard question?
Please, tell me at least "Yes, you're right" or "No, you're wrong".