How does atmospheric scattering explain the faintness of starlight?

[neelakash]

Homework Statement

"Explain the statement that one's eyes could not detect the faint star-light if light were not particle like"

Homework Equations

The Attempt at a Solution

What comes to my mind is that when light from outside enters the atmosphere,it gets refracted...referred to as atmospheric refraction.For this,light bends before it reaches the Earth surface.But,from a more realistic point of view,this bending is a scattering rather than a refraction.

If we look upon the atmosphere as a continuous medium with constant refractive index,the idea of refraction is correct.We might see the refraction using light as an EM wave.
But, basically, the air is not so.Its density, pressure etc. changes with time.Thus, we know it is composed of air molecules and what we know as refraction,is more precisely, a case of scattering.

And when a scattering is involved, we know that the corresponding light can be treated as particles...[Compton Scattering]

---This argument has the virtue that, the wavelength is almost constant [remember that for visible light,Compton shift is negligible], yet it explains that the intensity is so small. By the action of scattering,many photons go away...they do not ultimately reach our eyes...and the observed intensity is much lower...

Please let me know what do you think about this problem.

 

[Dick]

Way off. The point is just that if light were not particle like, the energy would be spread over your whole retina evenly. It's not. Is that enough of a hint?

 

[neelakash]

So,you mean the faint star light refers to the spread of energy over a small part of retina?

If light were particle like, how can you be sure that energy will be confined to a small portion on the retina?After all,light still travels in straight line...and there should be no preferential selection of spot on retina where the image wil be formed.

 

[Dick]

Light is particle like. A faint blue light will distribute a few high energy photons over the retina. Rather than a continuous spread of low intensity energy.

 

[Dick]

You are posting quantum problems. You must remember the photoelectric effect?

 

[neelakash]

OK...this much I understand that the image of the star will be a small spot on our retina...the nerves connected to that portion of the retina will be excited...other will not...So,our brain will see the star.

But what is the problem with the wave model?The light reaches our eyes...has a plane wave front...and the wave normal is the ray direction...There will be an angle on the lens...like say 5' or so.Then, the lens converges the light beyond it...The light is focussed...and crosses over.The image will be still confined to a very small portion of the retina...
dY= angle x distance [since tan theta~theta at small angle limit]

So, how do you prefer particles over wave?

 

[Dick]

I think the intent of the problem is that you suggest the first answer (and it needn't be a small spot - it might be several neurons excited which are not terribly close to each other in either space or time). You can argue the your point that you can focus the light to the diffraction limit, but I think that's just missing the point. In the real world the detection mechanism is also quantum. I will grant you that the original question is really 'hypothetical' and I can't really even define what it means if 'light is not particle like'. What are the properties of the 'detector' then? Is it a radio? I think you are stretching the question beyond the intentions of the questioner.

 

[neelakash]

The question was from Resnick's XII level book...I do not think his intention is to make us involved in the detailed analysis of interaction of light with retina and then with the nerves.
He wants some logic that light should behave like a particle if we are to see the faint star lights...

First of all,I do not see how photo-electric effect comes into consideration.

Secondly,I am not dis-believing what you say.But there is not enough logic so far in your argument that discards the wave alternative.

There will be an angle on the lens...like say 5' or so.Then, the lens converges the light beyond it...The light is focussed...and crosses over.The image will be still confined to a very small portion of the retina...
dY= angle x distance [since tan theta~theta at small angle limit]

One's eyes could not detect the faint star light...if the intensity of image were almost zero.That is appreciably no photon bombardment on the retina...

This is only possible,when light from the star is not reaching our eyes directly.Suppose,there is an obstacle...In such a case,the star light,could indeed reach our eyes following a roundabout path after suffering scattering many times, off the particles suspended in space, or off the gas molecules in the atmosphere.
This light still makes a small angle on the aparture of the eye...and the following processes occur...

 

[Dick]

Answer it as you wish.

 

[neelakash]

Since your logic is not sound,I did not accept it...Saying an answer is not sufficient if you cannot justify it...

 

[Marty]

I have some idea how the argument is supposed to go for photographic film, but I can't see how it would work for the eye. The problem with film is that we know we can build up an images from specks that appear sporadically, every few seconds or even farther apart if the telescope tracks the star as it moves across the sky. If we try to analyze this with the wave theory of light, we get into potential problems with the power density being very low at the point of detection. But for the naked eye, it's different. We don't normally see sporadic photons...stars might "twinkle" a bit from atmospheric effects, but basically the astronauts in outer space looking out the window see tiny, steady glowing points of light. So there must be enough photons-per-second (10,12 at least?) to maintain the illusion of steady glow. How is this inconsistent with the wave theory of light?

 

[Dick]

It's not. The problem is that, looked at in detail, the nature of the question requires you to construct an alternate universe to answer it. It's really hard to go into specifics of "what if light weren't particle like". That's about it. It's a really poor question.

 

[epenguin]

It may be a "poor question" if you consider it a close-ended one. If it is just meant to elicit some thought and knowledge perhaps we should call it a hard question rather than a closed one.

A thought that occurred to me is that Maxwell worked on vision as well as a wave theory of light. He did not give a quantum explanation - he must have been stupid!

It is possible, a bit oversimplifying, for the eye to detect single photons. You can find stuff just googling "sensitivity vision photons". Detecting a single photon flash is not the same as 'seeing starlight' though but might be relevant.

The nerve impulse are triggered by a single photochemical reaction (a cis-trans isomerisation) in single cell AFAIK, and the reaction and much of the amplification mechanism is known. The knowledge is relatively recent - there is a huge amount of it, mostly detail irrelevant to your question, but an outline of the visual process should be part of the culture of the physicist as it is a tradition.

 

[Marty]

It's not. The problem is that, looked at in detail, the nature of the question requires you to construct an alternate universe to answer it. It's really hard to go into specifics of "what if light weren't particle like". That's about it. It's a really poor question.

I kind of agree with egpenguin here. We ask a similar question if we say "explain the statement that we could not obtain the photoelectric effect if light were not particle-like." Technically, this question also requires the we construct an alternate universe to answer it. But we routinely make just this argument.

So I think the question stands: does the sensitivity of the eye with respect to distant stars serve as evidence for the particle nature of light? I don't think it does. As I said in a previous post, I think there's potentially a stronger case for the sensitivity of photgraphic film, but I don't think the analysis is obvious or trivial.

 

[NYSportsguy]

The statement above that this guy starts out with is false to begin with. Not sure why we are even having this discussion.

 

[HallsofIvy]

You are posting quantum problems. You must remember the photoelectric effect?

Which says that light must have a certain minimum energy in order to cause an electron jump and so stimulate a nerve. This question has nothing to do with "scattering" or "diffraction".

 

[Marty]

Assuming the first poster had a right to put up the question on the basis that it came from a book and he wanted help in coming up with an answer, at what point exactly do you think the discussion should have ended?

Just wondering.