# Aberration of light in classical and relatvistical cases

#### queenstudy

i need someone to explain me the aberration of light , i tried to read i from my book its a bit more complicated than i thought i mean when we move the microcope we make a tilt what do you mean by that???
all in all i didnt understand this concept and i need a really clear explaination especially that our professor didnt come in the last week , when we needed him the most before the exams please help and thank you

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#### jtbell

Mentor
when we move the microcope
What microscope?

Can you describe the apparatus and observations in more detail? Don't assume everybody has read the same book that you have.

#### Qzit

Hi queenstudy.
I do not know about your book either but I can give you a very basic idea of how I understand aberration of light. Instead of light let’s think of one photon. Basically aberration of light means the change in frequency of light. Let’s say we have a photon with a 0.9 Nano second light speed length when produced at a rest frame. If a photon emitter creates photons in opposite directions (in space at a resting frame) the photons will have the same length. Let’s also say this is in the middle of the visual range. Now we will take that same photon emitter in space to ½ the speed of light. The photon created in the forward direction of travel will have a 0.06 Nano second light speed length. This is because of the forward direction at the beginning of the photon creation and the end of the photon creation the space ship contracted the rest frame photon by 1/3 of the photon distance. In the back of the emitter the photon is elongated and has a photon length of 1.2 Nano light speed length because the emitter moved away at ½ the speed of light. The back is considered red shifted and the front is considered blue shifted. The shorter the length of the photon the more energy it carries. This may or may not be what happens but it is a way of thinking about the aberration of light.

#### queenstudy

sorry for the misunderstanding okay?
the aberration fo light was discovered by bradley in 1727 where he observed that the stars appear to move in circles
he imagined that the observer(who is at the surface of the earth and telescope as well moving to the right with spped v)
so inorder for the light, coming from the star, to pass down the telescope tube without hitting its sides , we should tilt the telescope by an angle alpha
do you want me to explain more or is it enough? i want to know how did he get alpha?
where tan(Alpha)=v/c where v is the speed of earth and c is the speed of light(star)

#### Doc Al

Mentor
Basically aberration of light means the change in frequency of light.
No it doesn't. Aberration of light has to do with the angle that the light makes, not the frequency.

#### queenstudy

right so can you help me out please about classical and relativistical aberration?

Mentor

Mentor

#### Bill_K

Doc Al and jtbell, I must dissent.

I've always thought of special relativity as a simple subject, where the answers fell out almost automatically. Until, that is, I came to Physics Forums and read some of the 'explanations' offered! The goal, it seems, is to do it all without using the appropriate mathematics. Special Relativity is about four-vectors. With the use of four-vectors, most SR problems have a similar formulation and a quick solution.

But instead I see rambling multi-page verbal descriptions, with step after step and diagram after diagram. Maybe I have an unusually short attention span, but I tend to pass out halfway through such things. An analogous endeavor would be to attempt to explain the levels of the hydrogen atom without using the Schrodinger equation. And in fact, some people do try to do that! And it all looks like magic. But the most serious drawback is that nothing is learned. If you don't build the foundation of a uniform approach, the next problem will look just as challenging as the last.

Deriving the relativistic aberration is a one-liner. (Well Ok, maybe two.) A light ray is described by a propagation vector k = (kx, ky, kz, kt). Under a Lorentz transformation,

kx' = γ(kx + v/c kt)
ky' = ky
kz' = kz
kt' = γ(kt + v/c kx)

If the ray is propagating at an angle θ with the x-axis, k = (k cos θ, k sin θ, 0, k), and

kx'/ky' = γ(kx + v/c kt)/ky
⇒ cos θ'/sin θ' = γ(cos θ + v/c)/sin θ

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