Cross-polarized crystal of 'Floralife Crystal Clear'

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ChrisR
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Post by ChrisR »

Citric acid xtals growing, by Ralf Wagner:
https://www.youtube.com/watch?v=doo9JGpVJvQ
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Post by Smokedaddy »

... looks great with my Pocket 3Dvu glasses.

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Post by banania »

mtuell wrote:Pau is essentially correct. I'm not sure about the solid/liquid aspect, but I can't think of an example of a chiral solid at the moment. Certain liquid crystals are chiral, notably our friend cholesterol (a cholesteric liquid crystal).

Optical activity as a term is generally reserved for substances with circular birefringence, which rotates the plane of polarization. Linear birefringence, on the other hand introduces a phase shift between linear components, turning the polarization state (in general) elliptical.

You can tell the difference if you rotate the sample between crossed linear polarizers. Linear birefringence will have a pair of axes (fast and slow), which if the input linear polarization is aligned with one of them, no change is evident in the (mostly blocked) light going through the analyzer. In other words, you will see colors come and go as you rotate the specimen. On the other hand, if you are looking at optical activity between crossed polarizers, rotating the specimen won't have any effect since it is still rotating the plane of polarization the same way.

Mike
Mike, can you elaborate a bit as this is very intreresting stuff. I believe I got a tip from you a couple of years ago about using certain cellophans as retarders. So thanks for the tip and please can you point out what is my mistake here:

If I place optically active stuff like cellophan wrap between polarizers and rotate the wrap the colors do change. I have built DIY wave plate retarders from these wraps and use and rotate them commonly when photographing birefringent (anisotropic) stuff like citric acid crystals. I can either rotate polarizer or the wrap or both. Tilting the slide in this setup also gives lots of new color combinations.

The colors visible in citric acid crystals between crossed polarizers are, I believe, interference colors, so it is a quantum phenomenon. Wave is split and other half is slowed down and when brought back together there is wave interference and this results in the colors we see. I believe all this can (could in theory) be calculated with the simple rules of Quantum electrodynamics.

Optical activity seems like a very different beast. There seems to be no interference going on, just rotating the plane a wave is oscillating, the exact amount depending on thickness of the optically active medium + the wavelength of the beam.

Sorry if this is confused, don't have the educaton, just like to play with this stuff.

Cheers, banania

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Post by rjlittlefield »

I am pleased to see the further discussion. :)

banania, it appears that your question has gone unanswered, so let me take a crack at answering it.

There is no need to invoke anything as subtle as quantum effects.

What happens is this:

1. The first polarizer filters the light source so as to yield light in which all wavelengths are linearly polarized in the same direction.

2. The second polarizer is crossed to block that orientation.

3. Birefringent material introduced between the two polarizers alters the polarization of light passing through it. Starting from zero thickness, adding material causes the polarization to become elliptical, progressing to circular, then elliptical again, and finally back to linear, with the same orientation as the original. Adding more material repeats the sequence.

4. Viewed through the crossed second polarizer, that sequence will be seen as initially black, then somewhat bright, brightest, somewhat bright, and finally back to black. With thicker material, this sequence repeats also.

5. And here's the catch! Different wavelengths of light go through this sequence at different rates.

As a result, only one wavelength will be extinguished (possibly several for thick material), while other wavelengths are still visibly bright.

Very thin material appears gray or white, as all wavelengths start getting through the sandwich to about the same extent. But as the material gets thicker, the short wavelengths reach extinction first. Blue is the first to go, producing a yellow appearance. The extinction notch continues through the spectrum: knocking out green gives magenta, knocking out yellow gives blue, knocking out red leaves cyan, knocking out infrared leaves something like a low saturation cyan, then blue goes out again (on its second cycle) taking us back to yellow, and so on.

I assume that somebody will correct me if I have messed this up. It's the first time I've tried writing an explanation of this effect, so that's completely possible.

--Rik

banania
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Post by banania »

Thanks Rik, trying to explain stuff is a very effective way to clarify thoughts. It just needs a student who doesn't seem to grasp the obvious and keeps asking stupid questions...

Here's what you wrote:

3. Birefringent material introduced between the two polarizers alters the polarization of light passing through it. Starting from zero thickness, adding material causes the polarization to become elliptical, progressing to circular, then elliptical again, and finally back to linear, with the same orientation as the original. Adding more material repeats the sequence.

Here's how I try to see this:

I put my eye on the path of light and see the frozen polarization vector on a certain plane as the linearly polarized beam slowly enters the birefringent material. I see the frozen vector splitting in two as it enters the birefringent material, each vector oscillating along different crystal axis at right angles to each other. The components of the split vector (ordinary and extraordinary waves) advance with different speeds along the different crystal axis and as the vectors emerge from the birefringent material, they are still at right angles with respect to one another. Hitting the second linear polarizer the components of these vectors that pass the polarizer are vibrating in the same plane, but out of phase as the slower one is retarded and so they interfere with each other (quantum stuff!) and this gives rise to the colors observed at the sensor/eye plane. And yes, different wavelengths of light go through this retardation at different rates.


What's wrong with the above picture? It is much simpler than yours (no elliptical phase etc.).

Another picture is this:

I put my eye on the path of light and see the frozen polarization vector on a certain plane as the linearly polarized beam slowly enters the birefringent material. I see the frozen vector starting to rotate around the path of the beam as it enters the birefringent material. I see different wavelengths rotated different amounts. When exiting birefringent material each wavelength is oscillating in different planes. Hitting the second linear polarizer these planes (wavelengths) pass the polarizer in different degrees and this gives rise to the colors observed at the sensor/eye plane. No quantum stuff here. What is the mechanism behind the rotation beats me so far...

I am not sure if these two pictures are contradictory or merely complimentary (or just plain wrong). What makes this difficult is the very variable usage of the term "optically active". Mostly "optically active" is defined as a substance that rotates the plane of polarization whereas "birefringent" is defined as stuff that separates the ordinary and extraordinary waves. These two, rotation and separation, seem like different things, but maybe they are really two facets of something more general.

Anyway, this is fun to try to figure out, emphasis on the word "try".

-banania

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Post by ChrisR »

There are some good YouTube descriptions, but as you say they look at one property and leave you wondering.

I can't find what I wanted to - I've changed computer so lost the bookmarks/history.

This one page is interesting, because it captures both optical phenomena (and some other ones along the way)
http://www.quartzpage.de/gen_phys.html

A useful stage of understanding for me was to "get" why, when you have full extinction from crossed polars, introduction between the two of another polariser at an intermediate rotation, will mean some light passes through the sandwich.

There's plenty I don't understand, but I won't raise those things here!

One confusing thing you see a lot is the "wave plate" stated to be eg "quarter wave". It's not a quarter wave, except at one wavelength. See from the Quartz reference how the rotation changes a LOT with wavelength.
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Post by Pau »

One confusing thing you see a lot is the "wave plate" stated to be eg "quarter wave". It's not a quarter wave, except at one wavelength.
Sure, usually it's computed for green 550nm. If not it wouldn't induce different colours and wouldn't have any utility for determining optical properties.
Pau

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Post by banania »

Reading again what Rik wrote yesterday it occured to me that I just need to connect the dots in my two pictures. Both pictures are more or less correct but tell just half of the story. Together they combine to make the story Rik told.

The principle of superposition of waves states that when two or more propagating waves of same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves. If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference.

As the two rays (fast and slow) oscillate along their respective crystal axis (on the same plane!) the vector sum rotates around the path of the ray - and amplitudes/wave crests of given directions grow bigger and smaller as the phase difference grows.

This means that, as Rik put it, " Starting from zero thickness, adding material causes the polarization to become elliptical, progressing to circular, then elliptical again, and finally back to linear, with the same orientation as the original. Adding more material repeats the sequence."

Yes, the frozen rays are separated and have phase difference which explains the interference colors but the rays also travel in time with the sum vector rotating around the direction of the wave axis, and this also explains the interference colors. Both pictures, separation and rotation, are fairly valid, they are just looking at the propagation of light from different perspectives.


The dots are better connected now, I hope...

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Post by ChrisR »

Quote:
One confusing thing you see a lot is the "wave plate" stated to be eg "quarter wave". It's not a quarter wave, except at one wavelength.
Sure, usually it's computed for green 550nm. If not it wouldn't induce different colours and wouldn't have any utility for determining optical properties.
Yes, so EG 1/4 wave is not what one might think. Also standardised presumably, is how much the plane of polarisation gets rotated per change in wavelength.
If you look at the numbers for Quartz, it's very sensitive at the UV end of the spectrum.
I imagine other crystals would give different rates. This could be why the mineralogists' plates use different material, after which they are named?


This stuff is all probably well documented in a 100+ year old book I don't have...
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Post by rjlittlefield »

banania wrote:Reading again what Rik wrote yesterday it occured to me that I just need to connect the dots in my two pictures. Both pictures are more or less correct but tell just half of the story. Together they combine to make the story Rik told.
I'm glad to hear that my explanation made sense after more study. (One indicator of good students is that they actively work to resolve inconsistencies between different explanations.)

On review, I see one flaw in what I wrote. I said that "...become elliptical, progressing to circular, then elliptical again..." But in fact it will hardly ever become circular. To achieve circular requires that both components of the wave have equal magnitude, which happens only when the first polarizer happens to be lined up at exactly 45 degrees from each axis of the crystal. In all other cases, even when the phase shift reaches 1/4 lambda the rotating wave will still have high and low magnitude axes so it will still be elliptical rather than circular.

In practice, this will become apparent in cases where the first polarizer is closely aligned with one of the crystal axes. When that happens, we only ever get a small component in the orthogonal direction, the one that will be passed by the second polarizer, so that section of the crystal will remain dark.

I believe this is why, in my initial image, the sections of crystal pointing to 11 o'clock and 8 o'clock are notably darker than the ones with orientations midway between those.

Image

Both pictures, separation and rotation, are fairly valid, they are just looking at the propagation of light from different perspectives.
I think that's true in this particular case.

But in my opinion, it would be a significant loss to explain this effect solely in terms of orthogonal axes, omitting mention of elliptical polarization.

The reason for that opinion is that the concept of elliptical polarization is very handy for explaining & understanding an assortment of other phenomena that would otherwise be intractable.

An example is 3D movie projection. Think about it: those magic glasses somehow manage to separate the left-eye and right-eye views, and they continue to do that even when you tip your head. With linear polarizers, say left-45-degrees and right-45-degrees, you would get good separation with your head vertical, but ghosts would appear with the slightest tip of your head. The trick is that the glasses are circular polarizers, one left and one right, and similarly the two images are circularly polarized, one left and one right.

Of course, if you're careful enough, the behavior can be explained in terms of orthogonal vectors and phase relationships. But I'll submit that doing all those manipulations accurately enough to get the right result regarding head tip is a lot harder than thinking in terms of circular polarization.
and so they interfere with each other (quantum stuff!)
I think we disagree regarding this word "quantum". You like to use the word here, and I don't.

To explain my position...

First, I'm pretty sure that the idea quantum relationships are essential in this problem, or even very helpful, would feel very strange to the people who figured out about polarization back in the 1800's. That was long before quantum mechanics even had its start around 1925 and even longer before quantum electrodynamics appeared, a couple of decades after that. You definitely do not need quantum anything to understand about interference phenomena.

Second, I don't see any of the essential features of "quantum-ness" in this problem -- in particular there's no restriction to a finite number of energy states, no sense of quantum uncertainty, not even a need for particle-wave duality. All you need for pretty good understanding is basic wave theory in a continuous domain.

Now, I will happily agree that if somebody gives you the crystal structure and asks you to compute its effect on polarized light, from first principles, no recourse to experimental data, then quantum electrodynamics may be just the tool you need to do that. But I will also predict that after a great deal of calculation, the key result you'll get is that there are principal axes, how they are physically aligned with respect to the crystal structure, and what refractive index values go with them. In other words, you will have gone to a great deal of trouble to rediscover birefringence.

There's some tension in my thinking here. On the one hand, I like introducing the concept of elliptical polarization, and part of me desperately wants to say that "One should never pass up an opportunity to introduce a useful concept". But on the other hand, quantum effects are also useful concepts, so why do I not want to use them here?

I think it's a matter of relevance. Elliptical polarization seems pretty simple and applies directly. Quantum effects are neither of those, and worse, I think they quickly lead you down a rabbit hole of distractions. After all, we know from quantum theory that each photon will get absorbed at exactly one physical place. Aside from incidental losses, that place will be either in the first polarizer, the second polarizer, or the image sensor. But all photons getting through the first polarizer should somehow be "the same". How does it happen, then, that in the actual device, some of those photons end up depositing in the second polarizer while others get through to the sensor, in exactly the same proportions that are implied by wave intensity in the continuous models? Sorry, I don't think I want to go there!
trying to explain stuff is a very effective way to clarify thoughts.
Dang, busted! Yes, I frequently write explanations for that very reason.

Sometimes it also has the effect of changing thoughts.

A striking example comes from when I first taught remedial algebra to first year college students who had forgotten what little math they ever knew. Prior to that experience, I generally fired up algebra whenever I wanted an answer to some simple math problem. But after explaining the process a few times, I realized that in most cases I didn't actually want a general symbolic answer, but rather just a single number relevant to the particular problem at hand. Of course that second case admits a much wider range of solution techniques involving numerical methods, most of which are much simpler as a matter of practice than slogging through the symbol manipulation. The result of that insight was that I ended up rewriting the algebra curriculum so as to include numerical tools such as Excel's Goal Seek and Solver tools. I also found myself doing a lot less algebra and a lot more Solver'ing in my own work.

Bear in mind, my first college degree was in Numerical Analysis. You'd think that reaching for those techniques would have been a natural thing to do all along. But the tools had evolved, and I had not taken the time to rethink my processes. Writing the explanations solved that problem I didn't even know I had.

--Rik

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Post by ChrisR »

Off-topic here, but as someone recently introduced to teaching as a hobby in retirement, I'm fascinated by why some students understand immediately, and others only see a red fog. As a lad I was often in the red fog group, getting very upset :smt005 when a teacher demanded to know why I didn't understand.

Today Youtube is such a blessing, there's always another way to get to the same end.

Man in white coat with cool props waving his arm around:
https://www.youtube.com/watch?v=ycY2mUZHS84

Nice simple graphics
https://www.youtube.com/watch?v=Fu-aYnRkUgg

Cool graphics
https://www.youtube.com/watch?v=8YkfEft4p-w

(there are better ones with similar graphics, which I haven't re-found)

A talking head (female, they're different imho) and at last :idea: a mention of an achromatic waveplate
https://www.youtube.com/watch?v=NkfLOUr2Z3g

Slowly it's sinking in, there are still cloudy patches...
Chris R

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Post by rjlittlefield »

Man in white coat with cool props waving his arm around:
https://www.youtube.com/watch?v=ycY2mUZHS84
Excellent -- I love the snippet from 3:40 to 4:00, where he physically rips apart the 3D glasses and peels off the quarter-wave layer.

--Rik

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Post by grgh »

04.20 am. two days after major heart surgery.
started reading post, got caught up in all replies,
pains and aches disappears, shall be researching for hours.

all because of a lovely photo that caught my eye and imagination.

no wonder we all love this site.

george
used to do astronomy.
and photography.
Zeiss Universal Phase contrast.
Zeiss PMII

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Post by rjlittlefield »

grgh wrote:04.20 am. two days after major heart surgery.
started reading post, got caught up in all replies,
pains and aches disappears, shall be researching for hours.

all because of a lovely photo that caught my eye and imagination.

no wonder we all love this site.
You have made my day -- I am very pleased to help provide such good medicine. :D

Heal quickly!

--Rik

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Post by Rikisub »

Absolutely amazing, specially the stereo!

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