Labs: Refractive Index and Resolution

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Labs: Refractive Index and Resolution

#1 Post by linuxusr » Mon Jan 17, 2022 1:30 am

The purpose of this post is to invite discussion on Refractive Index (RI) and to understand it in and of itself, as well as its relationship to resolution and the medium and the specimen. Specifically, for the purposes of the labs described here, think of this three part relationship: the RI of glass (slide and coverslip); the RI of the medium, glycerol versus water; and the RI of the protein keratin in human hair (the specimen), one purpose being to assess the difference between the resolution of the specimen using glycerol versus water.

The idea for this post, and the labs, are taken from Thompson and Thompson, "Illustrated Guide to Home Biology Experiments" (O’Reilly, 2012), 64,65.

The three labs are simple to execute but their ramifications are not simple, for they describe the behavior of light. Some of the theoretical stuff will be explored after presenting the labs, for example, a formal definition of refractive index, presented in clear terms, will be useful. For now, “bending of light” will serve as a functional definition for refraction. Index of refraction adds another component that will also be explored.

It is useful to begin with some RI values as these will be used and referenced in the labs, however, without worrying at this time exactly what they mean.

The baseline value for RI is the number 1. This is the value given in a vacuum. I suspect that this means that there is zero refraction because there is no medium that would otherwise deflect light passing in a straight line. We at MH are LM users and we hear that the RI value of air is 1. This value has been rounded down. The actual value is 1.000293 or 1 + 293/10000. Apparently, this seemingly minute value is significant for electron microscopy since EM requires a vacuum when viewing a specimen.

Values for First Lab

Glass rod, slide and coverglass ~ 1.5
Water 1.3

First Lab

Fill a beaker with water and place a glass rod in it. Observe the rod.
Result: Unsurprisingly, you see the glass rod as you would expect it to be.

Values for Second Lab

Glass ~ 1.50
*Glycerol 1.47

*You can substitute vegetable oil for glycerol which has the same or nearly the same RI.

Second Lab

Same procedure except substitute glycerol for water and observe the rod. Result: Surprisingly, the rod disappears or nearly disappears! But why? It must have to do with differences in the RI’s but what that signifies in terms of the behavior of light is yet to be determined, hopefully, in the theoretical part of this post.

However, some inferences can already be made. In the case of the “invisible” rod, the difference between glass (1.5) and glycerol (1.47) is 0.03, a nearly imperceptible difference. It appears that if two media have the same RI that light proceeds in a straight line, does not bend, and that the media cannot be distinguished.

In the case of the visible rod, the differences in the RI’s are much greater (0.2) or 20/100’s versus 3/100’s in the former case.

Values for Third Lab


Glass 1.50
Water 1.30
Glycerol 1.47
*Keratin 1.52

Or glass, keratin and water versus glass, keratin, and glycerol.

*Keratin is the protein in hair.

Third Lab

In this lab, instead of using a glass rod, substitute a human hair. (My sample used European hair from the head.) Observe one hair specimen at 400x TM using water and the other using glycerol. Try to keep all variables constant (e.g. lighting, focus); photograph and compare the results.

Compare the two images:

A. Keratin (1.52) and water (1.30)

[media] Image [/media]


Here, just like with the glass rod and water, the significant difference in RI’s, should enable the keratin (of the hair) to be clearly visible. And so it is.

B. Keratin (1.52) and glycerol (1.47)


[media]Image [/media]


For me, this lab gave an unexpected result. In spite of the RI values being similar the hair does not appear “invisible” or nearly so, as expected. Any thoughts?

Turning now to the theoretical part, that is, defining refractive index with respect to the behavior of light. “Index of refraction,” is a compound concept including (1) refraction and (2) index of refraction. Starting with refraction, following is a paraphrase from Julian P. Heath, "Dictionary of Microscopy" (Wiley, 2005), 269.

It is true that “bending of light” is a satisfactory simple definition. However, to add, the light bends at the interface between two materials (e.g. keratin and glycerol) but bends or refracts only when the angle of incidence is > 0°. (More on this later.)

What is the angle of incidence? The same dictionary defines angle of incidence as “The angle formed by a ray and a normal (perpendicular line) at the point of incidence.” (p. 30) First, why can the angle of incidence not be 0°? From Douglas Downing, "Dictionary of Mathematics Terms" (Barron’s, 2009), 10, imagine a fixed ray 1. Fixed ray 2 has the same end point as fixed ray 1. If you rotate ray 2 until it merges with fixed ray 1, then there is no angle (zero degrees) because for there to be an angle there must be separation between the rays greater than 0°.

Returning to angle of incidence, it is “The angle formed by a ray and a normal (perpendicular line) at the point of incidence,” see this diagram:


[mediaImage][/media]

From Macura, Wiktor K. "Angle of Incidence." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. [https://mathworld.wolfram.com/AngleofI ... _material


It confirms my earlier speculation as to why one cannot see the glass rod. Finally, it also explains a relationship between RI and resolution which had not been clear to me. This relationship is confirmed in the formula for NA (Numerical Aperture):

[media][Image/media]

In this formula and in the diagram you can see n subscripts 1 and 2, respectively, which represent the two media by which light is refracted, and whose values must be entered into the formula to evaluate the NA.
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Re: Labs: Refractive Index and Resolution

#2 Post by MichaelG. » Mon Jan 17, 2022 9:17 am

linuxusr wrote:
Mon Jan 17, 2022 1:30 am
The purpose of this post is to invite discussion on Refractive Index (RI) and to understand it in and of itself, as well as its relationship to resolution and the medium and the specimen. […]

The baseline value for RI is the number 1. This is the value given in a vacuum. I suspect that this means that there is zero refraction because there is no medium that would otherwise deflect light passing in a straight line. We at MH are LM users and we hear that the RI value of air is 1. This value has been rounded down. The actual value is 1.000293 or 1 + 293/10000. Apparently, this seemingly minute value is significant for electron microscopy since EM requires a vacuum when viewing a specimen.

[…]
.

A very interesting post, linuxur … But [at least for comprehension, even if not for our practical purposes], I think we need a good description of Refractive Index as our baseline.

It is a dimensionless ratio … which is, of course, why the value for a vacuum is 1
https://spark.iop.org/refractive-index

Regarding the RI of Air … I know of no better document than this one :
https://emtoolbox.nist.gov/wavelength/documentation.asp

… and would particularly recommend noting the ‘Simple Shop-floor Formula’ !
https://emtoolbox.nist.gov/wavelength/D ... #AppendixB

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Re: Labs: Refractive Index and Resolution

#3 Post by Hobbyst46 » Mon Jan 17, 2022 11:27 am

linuxusr wrote:
Mon Jan 17, 2022 1:30 am
we hear that the RI value of air is 1. This value has been rounded down. The actual value is 1.000293 or 1 + 293/10000.
Actually 1.000293 = 1 + 2.93/10000

More importantly, I am trying to understand the two images.
They look as if exactly the same field of view is shown. The same region of the hair, exactly.

Since it would be difficult to impossible to get the same FOV after the mounting liquid is switched (the liquid in which the hair is mounted, under the coverslip), I believe that the "lab 3" is not the same as "labs" 1 and 2.
In lab 3, was the immersion fluid switched from water to glycerol ? if so, the difference between the RIs of the hair and the liquid is irrelevant.

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Re: Labs: Refractive Index and Resolution

#4 Post by Microscopy_is_fun » Mon Jan 17, 2022 3:51 pm

Hi linuxusr,

when you talk about imaging of microscopic objects, you need to distinguish between amplitude objects (AO) and phase objects (PO).

AOs modify the amplitude of light passing through them by absorbing certain wavelengths of the incident light. POs modify the phase of the incident light with respect to the light passing the surrounding media by slowing down the light due to their higher refractive index. The example of your glass beam is a typical PO, since glass is very homogeneous and does not absorb visible light. When you match the RI of the media to that of the colorless glass, the glass becomes invisible since the light passes equally fast through glass and medium, respectively.

Hair is, in contrast to glass, a very complex, heterogeneous system made of microscopic fibres and many interfaces between the constituents of the hair. Hair is also colored, meaning it is a PO as well as an AO. Within the hair you might observe not only refraction of the incident light beam, but also absorption, scattering and/or polarization phenomena. It is therefore no big surprise theat hair is still visible in a refractive index matched medium.

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Re: Labs: Refractive Index and Resolution

#5 Post by linuxusr » Mon Jan 17, 2022 6:29 pm

@MichaelG
@Hobbyst46
@Microscopy is fun

Still getting back to you and reading your posts. Your responses are much appreciated. Meanwhile, I messed up and left out the following diagram, then one in which I reference the quadrants. Please re-read that part of my post in reference to this diagram:

[media]Image[/media]
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Re: Labs: Refractive Index and Resolution

#6 Post by Hobbyst46 » Mon Jan 17, 2022 10:03 pm

To try and simplify matters.

First, the numerical aperture is a property of the lens AND medium in contact with it. NA = n*sin(alpha), where n is the RI of the medium in contact with the lens. When the medium is air, n=1 to a good approximation. When it is water, n=1.33, etc.

Secondly, visibility depends on the difference of RI between media. Such as glycerol and water. There is a visibility index that can be calculated from the RIs (I forgot the formula unfortunately). From it, you predict whether the glass rod in the liquid in the beaker is visible or not. Nothing to do with resolution. It is not relevant to the hair experiment IMHO, as claimed in post #3 above.

Third, resolution is the ability to see separate objects in the image. Higher resolution is indeed achieved by a higher NA. Whether by using a high-RI medium, a "better" designed optics (for a larger sin(alpha) or both.

Four, an incident ray of light can hit a surface at any angle. However, as a rule, the lenses and specimen and detector and light source are all aligned normal (perpendicular) to a common axis, the optical axis, that passes through the centers of the optical elements. And, in many illuminations, there is ray that is collinear with the optical axis. It hits the surface at an angle of zero (by definition). Other rays hit at angles between 0 and 90.

Five, I believe that the last graph in your post #1 is taken from explanation of the NA of optical fibers, to explain total reflectance of light rays that hit the inner wall at the critical angle or beyond. Very different from the situation in "labs" 1 and 2 where light hits the beaker and its contents from all sides.

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Re: Labs: Refractive Index and Resolution

#7 Post by linuxusr » Tue Jan 18, 2022 6:06 pm

A very interesting post, linuxur … But [at least for comprehension, even if not for our practical purposes], I think we need a good description of Refractive Index as our baseline.

It is a dimensionless ratio … which is, of course, why the value for a vacuum is 1
https://spark.iop.org/refractive-index

Regarding the RI of Air … I know of no better document than this one :
https://emtoolbox.nist.gov/wavelength/documentation.asp

… and would particularly recommend noting the ‘Simple Shop-floor Formula’ !
https://emtoolbox.nist.gov/wavelength/D ... #AppendixB

MichaelG.
Thank you for these links, MichaelG. Hmm, I'm not sure any of them really add to the basic formula for RI which is, really, all that I wanted to flesh out. Sure, there are other parameters that can be added, such as wavelength.

I don't understand what is meant by "dimensionless ratio." Maybe I missed it. Can you tell me where it is defined or tell me how you understand it? For me, just on the surface, it seems like a contradiction. A ratio is a math construct. How can dimensionless(ness) even apply to a math concept? And, if it is physical space, how can space be dimensionless? It seems like even a point has dimension. The concept seems mind-boggling to me, much less how that ratio is supposed to equal 1. To me "1" is just a heuristic device to represent 0 refraction.

More concerning to me are some of the stuff I listed in "Loose Ends." For example, for our needs, it's important to understand the relationship between RI and resolution both for theoretical reasons, understanding these optics phenomena, but also for practical ones, like deciding when to use what medium if it makes a difference in the resolution of a specimen.

After doing some studying and writing this post, I feel that I still don't understand the relationship in a way that I can express clearly and concretely. I feel like it's on the tip of my tongue, that I almost have it but not quite. Can you explain it in a clear and concrete way? If so, you could really add to this thread. Explaining this relationship was a goal I had that I did not achieve.

.
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Re: Labs: Refractive Index and Resolution

#8 Post by linuxusr » Tue Jan 18, 2022 6:36 pm

Hobbyst46 wrote:
Mon Jan 17, 2022 11:27 am
linuxusr wrote:
Mon Jan 17, 2022 1:30 am
we hear that the RI value of air is 1. This value has been rounded down. The actual value is 1.000293 or 1 + 293/10000.
Actually 1.000293 = 1 + 2.93/10000

More importantly, I am trying to understand the two images.
They look as if exactly the same field of view is shown. The same region of the hair, exactly.

Since it would be difficult to impossible to get the same FOV after the mounting liquid is switched (the liquid in which the hair is mounted, under the coverslip), I believe that the "lab 3" is not the same as "labs" 1 and 2.
In lab 3, was the immersion fluid switched from water to glycerol ? if so, the difference between the RIs of the hair and the liquid is irrelevant.
Thanks hobbyst46. I entered your correction of my math into a calculator and converted to a decimal and got 1.00023, so I'm not sure what's going on here. Doesn't 2 begin the 10/ten thousandths place? Oh, I see an error I made. It should be 293 millionths. Anyway, expressed in language, the point is that refraction of light from air to glass compared to vacuum to glass, is extremely small, so much so that it can be discounted for LM but not for EM given that EM using the wavelength of the electron, no?

Leaving aside FOV for the moment, I'm getting confused over your lab comparisons. I don't blame you at all because the comparison I made in my post was a little confusing and hard to follow anyway. Cutting to the chase, when you compare glass in water versus glass in glycerol, the glass disappears in the glycerol but not in the water. It disappears in the glycerol because the RI's of the glycerol and the glass are almost the same, so there is almost no refraction. Now exactly why the human eye depends on refraction for an object to be perceived, I can't say. In the case of the glass rod in water, the rod is clearly seen because there is significant refraction.

The hair specimen repeated the same: difference in refraction and no difference in refraction. So why doesn't the hair disappear or at least become significantly less resolved like the glass rod? If the RI's are confusing, you can scroll back and see from the values that the hair and glass RI comparisons are analogous. The only difference is the specimen.

The only hunch I have is that according to the definition of RI, the refraction is in a transparent medium and the hair is clearly not transparent. The RI was for keratin (in hair) not hair per se, so maybe it was a badly written lab. If not a badly written lab, then I don't understand the point.
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Re: Labs: Refractive Index and Resolution

#9 Post by MichaelG. » Tue Jan 18, 2022 8:18 pm

linuxusr wrote:
Tue Jan 18, 2022 6:06 pm

I don't understand what is meant by "dimensionless ratio." Maybe I missed it. Can you tell me where it is defined or tell me how you understand it?
The ratio between two values which are expressed in the same units will inevitably be 'dimensionless' because it (itself) has no unit of measure ... The units cancel-out in the calculation,

RI = Speed of Light in a vacuum divided by Speed of Light in the material

Therefore RI is dimensionless

MichaelG.

.
By contrast ... Miles per Hour is a ratio : but the ratio has 'dimensions'
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Re: Labs: Refractive Index and Resolution

#10 Post by Hobbyst46 » Tue Jan 18, 2022 10:21 pm

linuxusr wrote:
Tue Jan 18, 2022 6:36 pm
Hobbyst46 wrote:
Mon Jan 17, 2022 11:27 am
linuxusr wrote:
Mon Jan 17, 2022 1:30 am
we hear that the RI value of air is 1. This value has been rounded down. The actual value is 1.000293 or 1 + 293/10000.
Actually 1.000293 = 1 + 2.93/10000

More importantly, I am trying to understand the two images.
They look as if exactly the same field of view is shown. The same region of the hair, exactly.

Since it would be difficult to impossible to get the same FOV after the mounting liquid is switched (the liquid in which the hair is mounted, under the coverslip), I believe that the "lab 3" is not the same as "labs" 1 and 2.
In lab 3, was the immersion fluid switched from water to glycerol ? if so, the difference between the RIs of the hair and the liquid is irrelevant.
Thanks hobbyst46. I entered your correction of my math into a calculator and converted to a decimal and got 1.00023, so I'm not sure what's going on here. Doesn't 2 begin the 10/ten thousandths place? Oh, I see an error I made. It should be 293 millionths. Anyway, expressed in language, the point is that refraction of light from air to glass compared to vacuum to glass, is extremely small, so much so that it can be discounted for LM but not for EM given that EM using the wavelength of the electron, no?

Leaving aside FOV for the moment, I'm getting confused over your lab comparisons. I don't blame you at all because the comparison I made in my post was a little confusing and hard to follow anyway. Cutting to the chase, when you compare glass in water versus glass in glycerol, the glass disappears in the glycerol but not in the water. It disappears in the glycerol because the RI's of the glycerol and the glass are almost the same, so there is almost no refraction. Now exactly why the human eye depends on refraction for an object to be perceived, I can't say. In the case of the glass rod in water, the rod is clearly seen because there is significant refraction.

The hair specimen repeated the same: difference in refraction and no difference in refraction. So why doesn't the hair disappear or at least become significantly less resolved like the glass rod? If the RI's are confusing, you can scroll back and see from the values that the hair and glass RI comparisons are analogous. The only difference is the specimen.

The only hunch I have is that according to the definition of RI, the refraction is in a transparent medium and the hair is clearly not transparent. The RI was for keratin (in hair) not hair per se, so maybe it was a badly written lab. If not a badly written lab, then I don't understand the point.
The rod in beaker experiments ("lab 1" and "lab 2"):
Let us start with - what is a transparent object ? a transparent object does not absorb light. in the terms of Microscopy_is_fun's post #4 above, it is not an amplitude object (AO). The clear glass rod is a transparent object, a phase object (PO). Were it a red or violet glass rod, it would have been both an AO and PO. The liquid around the rod is also a PO, as mentioned in post #4 above. Were the liquid (whether water or glycerol) colored, the rod would have been visible.

Yet we can see transparent objects in most cases. For example, when I stand a few cm away and facing a huge clear glass door of a building, I might crash into it, since I do not "see" it. When I see the same glass plate outside its frame, just hung in air, I see it because of reflections and refractions (and scattering from tiny imperfections, dust etc). So, indeed, the visibility of transparent objects relies on refraction and reflection (and other, weaker effects). These effects in turn are related to the RI. When the RI of the rod is nearly the same as that of the liquid, refraction is attenuated so the rod becomes invisible.

Note in passing that we are talking about the image of the rod. The rod itself never bent or break or relocate, regardless of the medium around it (air, water, glycerol, vacuum). Our brain transforms the slower speed of light in the glass (due to its higher RI) relative to the speed of light in air to relocation.

The hair experiment ("lab 3")
Regardless of the hair being different from a hypothetical pure keratin fiber, I am afraid that to understand what the experiment demonstrated, one needs to know how each of the two images was taken: in which medium was the hair mounted, was there a coverslip, and was there any immersion liquid between the coverslip (or bare specimen) and the objective front lens.

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Re: Labs: Refractive Index and Resolution

#11 Post by linuxusr » Fri Jan 21, 2022 11:09 pm

Microscopy_is_fun wrote:
Mon Jan 17, 2022 3:51 pm
Hi linuxusr,

when you talk about imaging of microscopic objects, you need to distinguish between amplitude objects (AO) and phase objects (PO).

AOs modify the amplitude of light passing through them by absorbing certain wavelengths of the incident light. POs modify the phase of the incident light with respect to the light passing the surrounding media by slowing down the light due to their higher refractive index. The example of your glass beam is a typical PO, since glass is very homogeneous and does not absorb visible light. When you match the RI of the media to that of the colorless glass, the glass becomes invisible since the light passes equally fast through glass and medium, respectively.

Hair is, in contrast to glass, a very complex, heterogeneous system made of microscopic fibres and many interfaces between the constituents of the hair. Hair is also colored, meaning it is a PO as well as an AO. Within the hair you might observe not only refraction of the incident light beam, but also absorption, scattering and/or polarization phenomena. It is therefore no big surprise theat hair is still visible in a refractive index matched medium.
Just getting to your post, Microscopy is fun. Thank you for this insight. First, I know that wavelength is one aspect of the refraction index. Do you think that the AO value affects angle of degrees? My guess is "no." However, it does seem that that is not true for PO, which indicates a phase change between two heterogeneous media, such as hair and glycerol, which means that there IS refraction and therefore the possibility of its index, whereas in the case of AO, homogeneous there is little to no phase change, refraction does not exist and RI is close to zero.

Do I have it right?

What do you think that this lab was trying to demonstrate by the inclusion of the hair? Why not just the two glass rod labs where the variation is between a specimen in a medium that refracts and in one that does not?

Another question: In this post I failed to understand a clear relationship between RI and refraction. Can you explain it. I feel that it's on the "tip of my brain" but I can't quite get it.

Oh, just re-read your last paragraph in which you stated that hair is both an AO and a PO. Still why would the images appear identical even when the media, glycerol versus water have very different RI's (PO's)? PO negated by AO?
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Re: Labs: Refractive Index and Resolution

#12 Post by linuxusr » Fri Jan 21, 2022 11:22 pm

MichaelG. wrote:
Tue Jan 18, 2022 8:18 pm


The ratio between two values which are expressed in the same units will inevitably be 'dimensionless' because it (itself) has no unit of measure ... The units cancel-out in the calculation,

RI = Speed of Light in a vacuum divided by Speed of Light in the material

Therefore RI is dimensionless By contrast ... Miles per Hour is a ratio : but the ratio has 'dimensions'
linuxusr:

MichaelG, do you mean this: If c is the speed of light, then c/c =1 (dimensionless), as if to say "undefined." Or pi/pi = 1
Ratio means division, so dividing one unit by itself, in a sense, smears out the unit's value.

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Re: Labs: Refractive Index and Resolution

#13 Post by linuxusr » Fri Jan 21, 2022 11:49 pm

Hobbyst46 wrote:
Mon Jan 17, 2022 10:03 pm
To try and simplify matters.

First, the numerical aperture is a property of the lens AND medium in contact with it. NA = n*sin(alpha), where n is the RI of the medium in contact with the lens. When the medium is air, n=1 to a good approximation. When it is water, n=1.33, etc.

Secondly, visibility depends on the difference of RI between media. Such as glycerol and water. There is a visibility index that can be calculated from the RIs (I forgot the formula unfortunately). From it, you predict whether the glass rod in the liquid in the beaker is visible or not. Nothing to do with resolution. It is not relevant to the hair experiment IMHO, as claimed in post #3 above.

Third, resolution is the ability to see separate objects in the image. Higher resolution is indeed achieved by a higher NA. Whether by using a high-RI medium, a "better" designed optics (for a larger sin(alpha) or both.

Four, an incident ray of light can hit a surface at any angle. However, as a rule, the lenses and specimen and detector and light source are all aligned normal (perpendicular) to a common axis, the optical axis, that passes through the centers of the optical elements. And, in many illuminations, there is ray that is collinear with the optical axis. It hits the surface at an angle of zero (by definition). Other rays hit at angles between 0 and 90.

Five, I believe that the last graph in your post #1 is taken from explanation of the NA of optical fibers, to explain total reflectance of light rays that hit the inner wall at the critical angle or beyond. Very different from the situation in "labs" 1 and 2 where light hits the beaker and its contents from all sides.
Hobbyst46 ET AL: I missed your post and I am reading it now. I had asked two other members to clarify the relationship between RI and resolution and I can see that that's what you are doing here. First, in NA = n*(alpha), what is the *? Second, I'm assuming that alpha here is Theta 2, the angle of refraction (see diagram above). Is that right? I want to paraphrase the formula is see if I'm understanding it correctly: So the angle of the refracted ray, as it changes angle of degrees from the incident ray, multiplied by RI = NA? Oh, oh! RI of which media? By definition there are two or there would not be refraction. I would think that it would be the second medium, the one through which the speed of light changes. It wouldn't make sense that it would be the first. It's a function: one input and one output.

Yes, as you state the difference in RI between two media, where the difference is greater than zero, there is visibility. These RI differences must be a range, I am thinking, with a beginning and and ending point (two RI values) which are the set of RI's visible to the human eye. You'd have to factor in visual acuity as well.

Are you saying that resolution pertains not to differences in visibility as a function of RI differences between two media but rather resolution refers to the ability of the human eye to distinguish discrete objects in a specimen through a microscope's particular optics when that specimen is viewed within one medium, for example, glass in a dry mount?

Please explain what you mean by the ray that is co-linear with the optical axis.

It's true that that one chart had to do with reflectance in optical fibers. I thought that I could ignore that aspect and use information pertaining to refraction.
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Re: Labs: Refractive Index and Resolution

#14 Post by linuxusr » Fri Jan 21, 2022 11:56 pm

OP:

@Hobbyst46
@Microscopy is fun

I now see there is a difference of opinion on AO and PO! (To be continued!)
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Re: Labs: Refractive Index and Resolution

#15 Post by MichaelG. » Sat Jan 22, 2022 7:33 am

linuxusr wrote:
Fri Jan 21, 2022 11:22 pm

MichaelG, do you mean this: If c is the speed of light, then c/c =1 (dimensionless), as if to say "undefined." Or pi/pi = 1
Ratio means division, so dividing one unit by itself, in a sense, smears out the unit's value.

.
Nearly … But the concept is much simpler that you appear to be making it

There is no ‘smearing’ involved … it is simply a ratio.

MichaelG.

.
This might help: https://physics.stackexchange.com/quest ... and-ratios
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Re: Labs: Refractive Index and Resolution

#16 Post by Hobbyst46 » Sat Jan 22, 2022 9:46 am

linuxusr wrote:
Fri Jan 21, 2022 11:49 pm

First, in NA = n*sin(alpha), what is the *? Second, I'm assuming that alpha here is Theta 2, the angle of refraction (see diagram above). Is that right?
Yes. " * " stands for multiplication. In words: for a given medium, NA equals the refractive index of the medium times the sine of the angle of incidence. And Snells' Law (now just 400 years old!!) states that the NA remains constant across the interface. That is why (writing n instead of RI) n1*sin(theta1) = n2*sin(theta2)
Please explain what you mean by the ray that is co-linear with the optical axis.
The ray that passes through the center of the lens and is normal to the lens's surface.
linuxusr wrote: ...and RI is close to zero.
This is a misleading phrase. By its definition, RI is at least 1. It is 1.00000...... in vacuum and >1 elsewhere. As explained by MichaelG, that the absence of dimensions (due to cancellation) does not annihilate the number (ratio or otherwise) in any sense.

Microscopy_is_fun
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Re: Labs: Refractive Index and Resolution

#17 Post by Microscopy_is_fun » Thu Jan 27, 2022 1:53 pm

linuxusr wrote:
Fri Jan 21, 2022 11:09 pm

Another question: In this post I failed to understand a clear relationship between RI and refraction. Can you explain it. I feel that it's on the "tip of my brain" but I can't quite get it.

Oh, just re-read your last paragraph in which you stated that hair is both an AO and a PO. Still why would the images appear identical even when the media, glycerol versus water have very different RI's (PO's)? PO negated by AO?
Hi linuxusr,

I think one issue you are facing in your understanding of optics is the fact that geometrical optics and wave optics are mixed in the discussions of this thread. Geometrical optics (or ray optics) are mathematically rather simple, and this model can be used to describe effects like refraction and reflection.

For a deeper understanding of all optical phenomena (e.g. phase objects, diffraction, resolution of a microscope, ..) you will need wave optics, which are mathematically somehow more demanding. Both approaches (geometrical and wave optics) yield the same results, but wave optics is broader and required for more advanced aspects of microscopy.

MichaelG.
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Re: Labs: Refractive Index and Resolution

#18 Post by MichaelG. » Sun Mar 13, 2022 10:20 pm

linuxusr

I’m resurrecting this topic, because you might find this new one interesting :
viewtopic.php?f=5&t=15147

MichaelG.
Too many 'projects'

Greg Howald
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Re: Labs: Refractive Index and Resolution

#19 Post by Greg Howald » Mon Mar 14, 2022 4:59 am

What a great and educational discussion. Thanks 😊 Now I have to get out my pencil. Greg

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