Labs: Refractive Index and Resolution
Posted: 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] [/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] [/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:
[media][/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][/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.
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] [/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] [/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:
[media][/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][/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.