# Rayleigh scattering not applicable to the double-slit experiment

In Rayleigh scattering a photon penetrates into a medium composed of particles whose sizes are much smaller than the wavelength of the incident photon. In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed. In this case, the scattering intensity is proportional to the fourth power of the reciprocal wavelength of the incident photon. (Emphasised by me.)

The explanation for the photon deflection is given like this:

Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency.

How is it possible to check that this interaction between the surface electrons of an edge and the grazing EM radiation does not lead to a quantised deflection of the radiation?

This is a badly formed article, imo.

This statement for example:

"particles whose sizes are much smaller than the wavelength of the incident photon"

confuses classical electrodynamics, size and wavelength , to photon existence, a quantum state. The photon has zero size and no wavelength, just energy. It is the classical em wave that is built up by many photons that has a wavelength.

How is it possible to check that this interaction between the surface electrons of an edge and the grazing EM radiation does not lead to a quantised deflection of the radiation?

For individual photons, it is a quantized deflection , that is why the single photon double slit looks random for small numbers. When you talk of "quantized" you need the photons.

The seeming randomness is calculable as a quantum mechanical probability of scattering "photons of given energy on two slits of given width and distance".

Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

One should be careful of the terms used.

• anna, I‘m a bit confused. Is the answer, yes, it is not applicable or not? Jan 18, 2021 at 18:29
• Ralley scattering is applicable in classical em. "predominantly elastic scattering of light or other electromagnetic radiation ". The double slit pattern can emerge from classical em waves, and photons are non existent in classical formalism,so the quoted position is wrong, it should not say "photons". Elastic scattering of photons , and the confusing them with wavelength is also wrong.. Photons do build up the classical wave and the mathematics may be ok for the penetration of classical em to the medium, but individual photons behave quantum mechanically. Jan 18, 2021 at 19:00
• So I would say that for the double slit R scattering is not relevant. at the photon level. Jan 18, 2021 at 19:01
• Rather, it is relevant only if it is written down quantum mechanically, as the compton effect , because essentially it is the elastic scattering off the photon over the collective electric fields at the edges of the slits Jan 18, 2021 at 19:20
• Thank you for your answer. I have to think about it a bit longer. Jan 18, 2021 at 20:48

Rayleigh scattering (RS) is primarily seen in gases where the particles have freedom of movement and they are able to interact with the photon wherein both particles have change in momentum. Wikipedia also states that RS can happen in transparent solids .... but there are many more solids where RS does NOT occur ... such as metals, any non-transparent solid, etc. By definition a slit is not made of transparent material.

In order to explain the double slit (DS) pattern (note that I do not like the word "interference") the Feynman path integral (PI) provides the most modern insight into the occurrence of the banding pattern. The Feynman PI says that we should calculate all paths and most importantly include a phase component. This calculation eventually concludes that the shortest path that is an integer number of wavelengths is the most probable one, sometimes the next longest path is chosen due to probability as well, i.e the second band. How the photon considers all paths could be a result of virtual photons, for example before a photon is even emitted an excited electron in an atom is already exerting EM forces thru the EM field ... and even all the neighbouring electrons and atoms are affected by the excited electron.

The DS experiment is one where the photon path is highly constrained starting with a very small light source, the 2 slits (or one) and finally the screen. This constraint is what shows or reveals the wave property of light and its harmonic nature .... we could say that the EM field must resonate like a piano string before the photon is emitted. Even single photons have wave properties (I do not know why some they do not) they are able to show color, be reflected or transmitted by an interference filter, and even in the DSE will or will not occur on certain areas the screen with great predictability.

The double slit interference/diffraction is usually derived using an approximation that the fields are scalars (so ignores any effects of polarized light) and that the opaque body containing the slits simply absorbs all incident radiation an does not affect the waves passing though the slits (Kirchhoff approximation). In reality the body is usually a conducting material that has induced currents and therefore scatters the radiation off the edges of the slits as well as allowing passaage though the slits. The full solution for conducting slits, and takimng into account the vector character of the E&M fields is quite complicated, but in the end differs little from the results of a scalar wave and an "opaque" body. There is a discussion of the more detailed theory starting on page 485 of the third edition of Jackson's Classical Electrodynamics together with a reference to an exact calculation by Smythe (Phys. Rev. D72, (1947) 1066.