I Rayleigh scattering -- What is the true reason for the color of the sky?

[hutchphd]

With respect to the OP, understanding the details of Rayleiigh scattering at an Intermediate level requires use of intermediate level physics. One sets up the salient physical process and does the math. This involves EM theory in 3 dimensions and integral calculus. It is not surprising when one has difficulty using intuition and pictures from the internet.
Despite good intentions, There is no royal path

 

[tech99]

It's more than an "analogy". It's strongly related. I'd say that the resultant amplitude A of the ray going to the observer will be something like:
A = A₀ X (1+cos²θ) . (1+cos²Φ)
where the angle θ is the angle between the incident ray direction and Φ is the angle between the scattered ray direction. (angles relative to the normal) and X is a 'small number', corresponding to the effective cross section of the molecule. I'm also doing this in 2D with the polarisation aligned with the dipole.
Not perfect because the size of the dipole is small relative to the wavelength and you don't get a perfect zeros for polarisation normal to the dipole.

The scattering dipole always lies in a principle plane containing the Sun and the observer. So there is no effect due to radiation pattern of the dipole - for a spherical scatterer the induced dipole is always normal to the Sun's ray. If, alternatively, we assume little rods, having random orientation, the polarisation purity will be destroyed due to re-radiation taking place with random polarisation, and this is not what is observed. If we resolve the Sun's radiation into two incoherent polarisations, and we consider the scatterers as spheres having induced crossed dipoles, then it accounts for all-round scattering and retains the polarisation effect observed. As the scattering loss of each particle is very high, it seems unlikey that double scattering is occurring to a significant extent, and the all-round scattering can be explained by the "unpolarised" nature of the Sun's radiation.

 

[sophiecentaur]

for a spherical scatterer the induced dipole is always normal to the Sun's ray.

Yes - that makes sense but are diatomic molecules spherically symmetrical? Maybe the random orientations takes care of that.

 

[tech99]

Yes - that makes sense but are diatomic molecules spherically symmetrical? Maybe the random orientations takes care of that.

Good point, so I presume these molecules will degrade the polarisation purity, because they can be canted at random angles.

 

[Salmone]

Don't we have to consider the unpolarized sunlight as two linearly polarized radiations with electric fields oscillating one orthogonal to the other in a plane perpendicular to the direction of the sunlight so that we can imagine two oscillating perpendicular dipoles which give the $1+cos^2(\theta)$ from the $sin^2(\theta)$ of the single oscillating dipole Poynting vector? This is what I've understood but I don't even know if you're talking about this.

 

[hutchphd]

None of this has anything to do with color. If you have a polarization question please start a new thread.

 

[sophiecentaur]

Don't we have to consider the unpolarized sunlight as two linearly polarized radiations

We sometimes choose to do that but the description of an elliptically polarised wave can be just that, with polarisation angle changing as the cycle progresses. It's like resolving forces - which we do or do not, according to when it suits us to solve a problem.

 

[tech99]

We must be careful to distinguish between elliptically polarised radiation and that from the Sun, which is called unpolarised. It can be resolved into any two orthogonal polarisations which are not related in phase, they are incoherent. With an elliptically polarised wave the two waves are in quadrature. Then we can find an exact cross polarised twin, but we cannot do so with the case of two cross polarised incoherent waves.