Why the sky is blue

Nu när det är så fint väder i Uppsala (kanske inte) så kan man ju passa på och göra ett blogginlägg om varför himlen är blå. För att man längtar till de dagar då himlen faktiskt är blå och inte full av vit/gråa moln.

Taget direkt från boken:
"The sharp frequency dependence of the power formula is what accounts for the blueness of the sky. Sunlight passing through the atmosphere stimulates atoms to oscillate as tiny dipoles. The incident solar radiation covers a broad range of frequencies (white light), but the energy absorbed and reradiated by the atmosheric dipoles is stronger at the higher frequencies because of the \omega^4- term in eq.  11.22. It is more intense in the blue, than in the red. It is the reradiated light that you see when you look up in the sky.

Beacuse electromagnetic waves are transverse, the dipoles oscillate in a plane orthogonal to the sun's rays. In the celestial arc perpendicular to these rays, where the bluness is most pronounced, the dipoles oscillating along the line of sight send no radiation to the observer (because the sin^2 \theta-term in eq. 11.21); light received at this angle is therefore polarized perpendicualr to the sun's rays.

The redness of the sunset is the other side of the same coin. Sunlight coming an at a tengent to the earth's surface must pass through a much longer strech of atmosphere then sunlight coming from overhead. Accordingly, much of the bluue han been removed bt scattering and what's left is red. "

eq 11.21 look like this:

<S> = ( ( \my_0 * (p_0)^2 * (\omega)^4 )/ ( 32 * (\pi)^2 * c ) ) / (  (sin\theta)^2 / (r^2)   ) * r-hatt

Explenation:
<S> is the pointing vector, look at wikipedia if you not familier with pointing vectors
\my_0 is a constant
p_0 is a dipoleconstant
\omega is the frequency
\pi is the same old pi
c speed of light
sin \theta is the term that describe the oscillating
r^2 is the radius
r-hatt is the direction of the pointing vector

eq 11.22 look like this:

<P> = ( \my_0 * (p_0)^2 * (\omega)^4 ) / ( 12 * \pi * c )

Explenation:
<P> is the total power radiated if you integrate <S> over a spherical surface
\my_0 is a constant
 p_0 is also a constant
\omega is the freqency
\pi is the same old pi
c is the speed of light

So now you have something to tell your friends when they ask you, aren't you following a physics program? Can you please tell me why the sky is blue.

So how did the \omega therm get there? It's from the start of how to describe when something is oscillating. And physics oscillations describes by ..... pamp, pamp, pamp,paaaa!

Cos ( \omega * t )

Ha en fortsatt trevlig lördag! Nu ska jag strax på Hubbertus middag=)