I was reading up on distortion of light due to air pressure differences and causing "puddle" mirages and fata morgana.
Also the "shimmer" effect of rising hot air.

Basically all the web sites said the reason for all this was the fact that the refractive index of air changes with air density.

I haven't quite figured out exactly why a greater refractive index at the ground level would cause a mirror image, but I do get the basic idea of the concept and will work on a more thorough understaning of the machanics at another time.

I do have a question, however.

Maybe no one has figured this out yet and that is why I can't find the answer on any of these pages, but I thought I would ask here.

Why does the refractive index of air increase with decreasing density?
Is there a defined principle at work here?

Sorry, i tried to draw a picture, but it wouldn't work.

Originally posted by one_raven
Why does the refractive index of air increase with decreasing density?
Is there a defined principle at work here? Are you sure you are not confusing the effect of air <i>density</i> with the effect of air <i>temperature</i>?

Even though the mass density is not generally consistent with the optical density, if you consider two uniform distributions of air at equal temperature, I think that the denser of the two will have a higher index of refraction. (I am also searching the net right now for the answer.)

Originally posted by errandir
Are you sure you are not confusing the effect of air <i>density</i> with the effect of air <i>temperature</i>?


I am not confusing density and pressure.
I mentioned hot air because, generally, hot air is less dense (therefore has a higher refractive index) which is what causes the "puddle in the road" mirage.

Originally posted by errandir
Even though the mass density is not generally consistent with the optical density
Explain, please.

Ha?
Shouldn't light travel faster via (at least) tranculent/transparent material with less density?
And refraction should have little to do with speed of light.... it's just because the light is refracted all the time that it reached your eyes later.....

Originally posted by curioucity
Shouldn't light travel faster via (at least) tranculent/transparent material with less density?

Why?

Am I wrong in assuming that Total Internal Reflection also plays a role in this "puddle in the road" mirage?

As in the earth's atmosphere acting as a prism with the layer of hot air near the ground being the reflective surface of the "prism"?

I am curious if anyone has ever placed a hot object in a vacuum to see if it had any of the "shimmer" refraction patterns above or around it at all.
I have been searching the net for this, but I just keep coming up with pages talking about what refractive index is.

Okay good shot.....

I just remembered Einstein's postulates; that speed travels at constant speed in VACUUM. Now think: Modern atomic models is described as hollow, meaning there is a lot of vacuum even in solid material, which means, there is nothing to stop light other than the 'massive particles' such as atomic nuclei.
Now back on the refraction: As light always travels at constant speed, the only thing that makes it seem to travel slower via different materials is the particles residing in the material (sorry, I lost some terms)..... Since it is 'very close to impossible' for these atomic particles to line up straight, there is a high chance that light will hit these particles often-> reflection in atomic level, refraction in our level. higher temperature means extra chaos to this atomic lining up, meaning that the chance that light hit the particles increases greatly.

I'm afraid that's a little unclear, so ask me about that which confuses you....

And about what you call Total internal refraction, I have no idea

Originally posted by curioucity
I'm afraid that's a little unclear, so ask me about that which confuses you....

No it is perfectly clear.

The problem I see with that idea is that, as you said, "it is 'very close to impossible' for these atomic particles to line up straight", therefore there could not be uniform refraction.

You also pointed out:
"Modern atomic models is described as hollow, meaning there is a lot of vacuum even in solid material, which means, there is nothing to stop light other than the 'massive particles' such as atomic nuclei."

Light photons, on the other hand are very small, right?

So the majority of the photons will get through, while some will get reflected by particles within the atomic structure.

However, that sub-atomic reflection wouldn't be refraction on the macro scale, it would be diffraction which is clearly evident when light passes through air.

I do understand (and somewhat share) your confusion, though.

If light moving slower in the Earth's atmosphere is attributed to the matter in the atmosphere (which is what I was told) then an medium with MORE dense matter should slow it down more.

There seems to be a missing piece of the puzzle.
(or maybe just the two of us are missing that piece. :))

Originally posted by one_raven
I am curious if anyone has ever placed a hot object in a vacuum to see if it had any of the "shimmer" refraction patterns above or around it at all.
I have been searching the net for this, but I just keep coming up with pages talking about what refractive index is.

It seems that it would not:
Vacuum Tower Telescope (http://www.sunspot.noao.edu/sunspot/pr/vtt.html)

OK.
This is really beginning to bug me now.

It seems that the more dense a medium is the greater the refractive index is:

Material n at 589.3 nm
(yellow sodium light) n (x-ray)

vacuum 1
helium 1.000036
air 1.0002926
carbon dioxide 1.00045
water ice 1.31
liquid water (20°C) 1.333
glycerine 1.4729
rock salt 1.516
bromine 1.661
glass 1.5 to 1.9
diamond 2.419


I was told in the past that this has to do with atoms absorbing and emitting photons.
The more dense the material is, the more closely the atoms are packed, therefore the more times it has to be absorbed and emitted by atoms, slowing it down.
I am not sure if this explanation is correct, but it sounded reasonable enough at the time.

Hot air, as we know, is less dense than cold air, right?
It would stand to reason that light would travel faster in hot air, not slower but every site I have read (probably a dozen or two now) have stated that the puddle mirage is caused by the drastic change in air density within a few inches above the road surface.
They say that light moves more slowly in hot air since it is less dense than cooler air, therefore having a greater refractive index. :bugeye: :confused: WTF?

What is going on?

they said that the puddle mirage is caused by light slowed down by hot water?
I can't say for sure.... but the only theory I know about it is that the closer air is to the earth during a hot day, the hotter (and thus less dense) it is. When light goes down in an angle from above, it is refracted to one extent that it gets almost parallel to the surface of earth. And supposedly, air layer which is too close to the earth gets far too thin, causing the downward refraction to fail to occur; instead, the light is then reflected upward and refracted so that it becomes less and less parallel to earth-> the puddle mirage is thus a reflection of the sky (or whatever up above).

As for your comment, about the 'hard lining-up':
Analogy: If you are to cycle between two rows of trees, can you go in a straight line if the rows of trees are not perfectly straight and parallel to your lane? Actually that was what I mean, but I don't know if either of us misunderstood the other.

Oh, and I also want to contradict my theory by adding up yours to mine:
Why is it that the refraction index of water is far less than diamond? In my theory, the more chaotic the particles in a matter is, the greater the refraction index-> perhaps I should have said diffraction index?

Why does the refractive index of air increase with decreasing density?

A wave travelling through a less dense medium will travel faster, if it is entering the change in density at an angle one side will travel faster than the other for a split moment whilst the other side is still in the denser air. So that the wave turns, this process continues as the wave travels downwards through lighter and lighter air and as one side of the wave is always in air of a lower density the wave will continue to turn and move back upwards untill it has left the area of fluxuation. Imagine a water ripple entering shallow water at an angle, it will turn towards the angle or if entering deeper water (hence easier movement) it will bend away from the angle.

I found something that looks pretty comprehensive.

I am leaving work soon, so I don't have time to read it all right now.

You can look at it in the meantime:

http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l1a.html

Originally posted by one_raven
I am not confusing density and pressure.Check again, I was contrasting density and <i>temperature</i>.




Originally posted by one_raven
I mentioned hot air because, generally, hot air is less dense (therefore has a higher refractive index) which is what causes the "puddle in the road" mirage.Yes, I would agree with this in the given context.




Originally posted by one_raven
Explain, please. I found a site with this concept mentioned, but I don't think anymore that it's very important. Basically, optical density is directly related to the time it takes light to travel through the material (in other words, it is directly related to the index of refraction). Mass density you probably already know. The site mentioned that these two densities are not necesarily directly related/proportional/or something, but, I don't think that this is relevant to the concern you are having.




My explanation of mirages:

On a hot day, the ground can be very hot, hotter than the air temp measured by most thermometers (i.e. it could be 100 deg outside, while the concrete or sand is hot enough to burn the bottom of your feet in rather quickly, around 150 deg or so, just pulling a number out of my ass). I don't know if you have experienced this personally, but I will go ahead and vouch for it. In this situation, the air immediately above the ground can be considerably hotter than the air further above the ground.

From what you have posted previously, I don't think that you'll disagree with the claim that this results in a decrease in air density closer to the ground.

This in turn results in a decrease in the index of refraction closer to the ground,

which in turn leads to the light traveling faster closer to the ground,

which in turn leads to the light curving upwards from the ground if it is incident at sufficiently shallow angles,

which in turn leads to you observing light from the sky hitting your eyes from the direction of the ground,

which is what water does, but by means of reflection, a different mechanism than refraction (though maybe not fundamentally).

I was just noticing the high end refractives in one raven's list--
glass 1.5 to 1.9 is classified as a liquid and

diamond 2.419 is a crystal lattice structure, isn't it?

Might have something to do with it...

Andre: it's odd that you can't see the ice or glass with relatively higher refraction index difference while you can see the boundary of cold and hot water probably with probably a very low difference in refractionation.
You could see it with thermography though couldn't you? But you are concerned with light, not heat readings...

Originally posted by Andre
Clear ice or glass below the water surface is just about invisible...This is not my experience. It is definitely clear, and so, in a way, it is always just about invisible, but I have always been able to see the ice/glass in the water. Glass is almost invisible in the air (if it is clean, there have been jokes centered around this fact), and the difference in the indices of refraction is even more pronounced in this case.

It is generally accepted that a mirage is <i>not a reflection</i>, but that it <i>is a consequence of REFRACTION</i>. There is no point in the light's path at which it encounters a stark boundary between regions of different temperature. If you wanted to, you could talk about the phenomenon on the atomic level, but there is no need; it makes perfect sense in the macroscopic model of light (along with the idea that the index of refraction decreases with temp).

I'll look for a reference in my spare time (for air, I'll let you find one for water). I will say right up front that the index will be quite insensitive to temp (maybe on the order of ppm, I can't remember off the top of my head). I probably wont get this to you today.

Firstly, I think that term "reflexion" is being missused in this web-site, or else the author is mistaken.

Secondly, I appologize, I thought that we were only talking about the kind of mirage that looks like a pool of water on the ground far away.

Originally posted by Andre
...reflection or light on a imaginary boundary between warm and cold.I'm sure that you didn't really mean this, but, I am going to clarify that light does not reflect off of imaginary boundaries.




Originally posted by Andre
For refraction difference the mass density change seemed not enough, since no optic anomalies occur between gasses of different densities at an orifice of a deflating tyre for instance.Actually, all optical phenomena are anomolous to some extent. We don't observe the anomolies in the case of the deflating tire, because this is an extremely small path distance compared to what is required for an observable anomoly. In the case of the mirage, it is the grazing light rays that are observed. These travel at least several miles (though, I don't know what a reasonable number of miles would be), all the while being curved under the infulence of the gradient of the index of refraction. It is easy to see how we would be able to observe the phenomenon in the mirage case, while not being able to in the tire case.




Originally posted by Andre
...I see that the mirage image seems to be upside down.
...
A mirror image is typical for reflection whereas with refraction you would have expected a double -upright- image. The upside-down image is due to the inversion of the temperature gradient at certain altitudes. There are several inversions/alternations of the temperature gradient from sea level to the mesosphere.

Originally posted by Andre
Please give a example where and how single refraction can produce a mirror image.Of course, for a real-world example, I would point to the fata morgana. Explanation of a simple, mental example, will be difficult without referring to a drawing, but I will give it a shot:

Picture two parallel light rays in the x-z plane, both in the +x direction. Now, picture a gradient in the index of refraction in the z direction. The light rays will be bent in the z direction, and the amount of bending will be proportional to the dot product of the gradient to the velocity of the ray. If the laplacian of the index of refraction is negative, then the two rays can be inverted.

what is going on here for so long.

ofcourse the mirage is a result of refraction and internal reflection. the layers of air above the surface of the earth are hotter then the layers above them and hence less dense and have lesser refractive indices. this makes any ray to bend like a loose rope hanging between two poles. effect is the mirage.

enjoy the sahara safari..




http://sol.sci.uop.edu/~jfalward/refraction/palmtreemirage.JPG

Originally posted by everneo
ofcourse the mirage is a result of refraction and internal reflection.I don't think that it has anything to do with reflection, and your picture doesn't seem to support such an idea, either.

One problem with the picture is that you cannot show inversion with only one ray. If the laplacian of the index of refraction is positive (and your picture does not indicate that it is not), then the image may very well be erect. I believe the laplacian will be negative, but that is not indicated on the picture, and we want to see an example of this.

hmm.. revisiting optics, especially total internal reflection, would be a nice idea.

Andre

Originally posted by Andre
Reflection or refraction.
Both.
Refraxion upwards out of the medium again is simply not possible due to the limit to horizontal. Remains the question if this was the correct scenario for reflection. For this it is still required for the refraction index to change with temperature.
critical angle is less than 90 deg so the the light rays would not get horizontal. the reflected rays start their upward journey through increasingly denser,less hot layers with increasing refractive index.

I'm back.

OK.
As I was saying earlier in this thread, all these sites claim that hotter air has a higher refrative index than cooler air.
Thatr doesn't make much sense to me, but for now, let's assume that is true...

I think the link to the animation (and accompanying text) off the first page I posted explains it very clearly and it totally makes sense to me now.

The Link (http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/waves/ltm.html)

If you accept this explantion, (which I do) it is reflection, not refraction.
However, since the reflection appears to occur in "mid-air" rather than at a visible tangible border, it appears to be refraction.

http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/waves/ltm.gif

This image clearly shows what is happening.
The incident wave is propagating in a medium (cooler air).
It encounters a border of heated air with a greater refractive index indicated by the thicker rope.
Part of the energy of that wave is propagated through the new medium.
The rest of the wave energy is reflected back through the original medium inverted and at a lower energy (of course).
It all makes perfect sense.

What doesn't make sense, however is how the hell could hotter, less dense air have a greater refractive index?

I am still looking for experimantal results of refractive index changes in air with temperature changes (or even just a chart verifying it) and can't find anything.

One,
Originally posted by one_raven
As I was saying earlier in this thread, all these sites claim that hotter air has a higher refrative index than cooler air.
Thatr doesn't make much sense to me, but for now, let's assume that is true...
don't assume that is true. it is false.

Originally posted by everneo
One,

don't assume that is true. it is false.

Trust me.
I have every inclination to believe it is false.

It only makes sense that it would have a lower refractive index as the temperature rises (all other things equal).

My problem is that I want to verify this with experimental results.

The only reason I said you should assume it is true for now was to illustrate what would be happening (reflection, rather than refraction) if all these sites were true about the refractive index of air decreasing with increasing heat.

I am reading more on the mechanics of refraction right now, but will get back to my search for a source of conclusive experimental evidence and a table, graph, equation or anything else resulting from those expriments that would verify that the refractive index of air does, in fact, drop with rising temperature.

It seems to me that if it can be verified that hot air has a lower refractive index (as it seems to) than cooler air then Total Internal Reflection (http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l3b.html) would have to be the culprit.

The greater the difference between the refractive index of the two mediums the greater the angle of incidence needs to be for Total Internal Reflection to occur (inverse-sine of the ratio of the indices of refraction See the math (http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l3c.html) ).
Since the difference of refractive indices between the surface air and the cooler air above it would have to be quite small, the angle of incidence would have to be quite large, therefore you would only see the "puddle" when you are nearly parallel to the hot road ahead of you.

I'm satisfied with that.

Now, If I could just get my hands on that chart that shows the refractive index of air in relation to air temperature, I could put this one to bed.


*edit* I just went back and read more in depth of what was posted, and basically I am saying what Andre was saying up there^.

Originally posted by errandir
There is no point in the light's path at which it encounters a stark boundary between regions of different temperature.

Perhaps not, but it does go through a quite abrupt temperature change in a very short distance just above the surface.

If it were a stark instantaneous difference it would be a mirror image as perfect as a glass prism.
But it isn't.
It is a shimmering mirror image due to the minor gradients in temperature (therefore minor gradients in critical angle of incidence) in that very thin "slice" of air.

First of all, my ice cubes are white inside, so they are easily visible in liquids. Even my European ice cubes are white inside ;) As the ice cubes melted in water, I observed bubbles, so I guess that might have been air suspended in the cube. So can we create a bubble-less ice cube? I'll have to play with that.

I think humidity could be a factor in the blacktop mirages but I am not sure there is moisture involved in desert mirages.

Refraxion = bending
reflexion = bouncing off some surface

Next: The highest mirage in North America
http://www.gi.alaska.edu/ScienceForum/ASF12/1224.html
Geophysical Institute, University of Alaska Fairbanks
Ned Rozell, is a science writer at the institute

"This type of arctic mirage differs from "inferior" mirages, those that occur in deserts or over hot road surfaces, because the air layers are reversed. In a desert or on hot blacktop, heated air lies at the surface, covered by a layer of cooler air. Since light rays always bend toward cooler, more dense air, objects appear to be lower than they actually are, often upside-down. The illusion of shimmering water on the highway ahead is actually the image of blue sky bending up to our eyes as it passes through different densities of air."

He is saying the light rays carrying the image towards our eyes, is bending or refracting.

But the issue of reflecting vs. refracting is what is taking place at the surface where the illusion is occurring?

Temperature and refraxion:
http://www.iop.org/EJ/abstract/0022-3727/11/8/007

The temperature dependence of the refractive index of water
G Abbate, U Bernini, E Ragozzino and F Somma
Istituto di Fisica Sperimentale, Univ. di Napoli, Napoli, Italy
Abstract. A direct determination of the temperature dependence of the refractive index of water has been performed in the range -3 degrees to +80 degrees C. In this range delta n/ delta t shows an exponential behaviour. Attempts have been made to obtain a relation between delta n/ delta t and the molecular polarisability of water.

URL: stacks.iop.org/0022-3727/11/1167
DOI: 10.1088/0022-3727/11/8/007
---------------
"Refractivity is symbolized by "N" and is a function of pressure, temperature, and vapor pressure (moisture). A result is that atmospheric refractivity near the earth’s surface normally varies between 250 and 400 N units (the smaller the N-value, the faster the propagation; the larger the N-value, the slower the propagation). Refractivity values become smaller with decreasing pressure and decreasing moisture, but larger with decreasing temperature."
http://www.tpub.com/content/aerographer/14271/css/14271_64.htm

http://tchester.org/sgm/analysis/peaks/refraction.html
The Effect Of Atmospheric Refraction On The Observed Elevation Angles Of Peaks
"Refraction is caused by two effects. First, light likes to travel on the path that gets to the observer in the minimum time. (Light is, after all, the fastest thing in the Universe, so you wouldn't expect it would like to take a longer path than it had to, right?) The speed of light is the speed of light in a vacuum divided by the index of refraction. Second, the index of refraction of the atmosphere depends on atmospheric pressure and amount of water present, which change with height in the atmosphere. Therefore light actually travels on a curved path in the atmosphere from one object to another. The path goes higher than the straight-line distance in order to take advantage of the faster speed higher in the atmosphere. Because the path is so curved, the observer must always look a bit higher to see the light rays coming back down from that higher elevation.

Clearly refraction must depend on some power of the distance. If you are observing something close by, light can't get to you any quicker by travelling very far upward. However, if you are far away from an object, light can take advantage of the faster speed at higher elevation and deviate more significantly from a straight line. "

The mirage on the road changes as you approach it...
-------------------

http://mintaka.sdsu.edu/GF/explain/atmos_refr/bending.html
Calculating Ray Bending

EXcellent picture with the sailboat showing reflexion in the mirage.

But the picture of the bus and car -- That does not look like a mirage, but a simple reflexion on a wet, or even a dry road.

http://virtual.finland.fi/finfo/english/mirage.html
Very interesting article.

it's been long since I last visited this thread, and now I feel outwitted. Well good for me anyway....