Thinness of the edge apex

[Jan]

For the BESS community it is important to understand the relationship between edge sharpness, BESS readings and thinness of the edge apex. Because the edge width of a DE razor blade is only 1/10 th of one micron we have no direct personal experience with such a very thin piece of metal.

On the other hand from personal experience we know that the sun light may be separated by prism into spectral colours. Each spectral colour can be associated with some wavelength of light. The wavelength of violet colour is approximately equal to the edge width of a sharp knife.
   

The visible spectrum goes from violet colour which has a wavelength of some 0.4 micron to red colours with some 0.7 micron.
   

When we measure BESS 200 gf on a sharp knife, we know that the edge width should be some 0.4 micron*. This edge width is equal to the wavelength of a violet colour!

Similarly, when we measure BESS 300 gf on a knife we know that the edge width should be some 0.5 micron, which is equal to the wavelength of a blue colour.

Jan

*P.S.: I.e. 4 times more than DE razor blade which has 0.1 micron edge width and 50 gf BESS.

[EOU]

Now that's an interesting way to think about it Jan! We're embarrassed that you were the one to make the association because that's the field (optics and lasers) that most of here share. I think we have it though - If you have to use a blacklight to see your knife edge (UV) it's very sharp and if you have to use an IR illuminator to see the edge it's very dull.    

We like to make jokes around here - we just don't make very funny ones.

[Jan]

EOU, you are correct!
Reading you reply I have realised that for most people both the thinness of the edge apex and the wavelength of blue light are beyond personal experience.

For me, who often plays with laser goniometer for edge angle measurements, it is slightly different. I have been thinking for a quite long time whether it would be possible to build a simple optical device for measuring the edge width. The laser beam could serve as an optical test medium. But so far I have no practical solution.

In the optical industry simple interferometry is often used to test the quality of surfaces.

[EOU]

Happy that you were able to see our humor (or attempt thereof) in our post Jan. We don't think that your idea is far-fetched or whimsical at all and, as a matter of fact, we have envisioned an  approach that might be feasible. Many moons ago we developed a simple and inexpensive means of coupling laser diodes to fibers via a GRIN lense. These are all very tiny things i.e. 9 micron fiber and even smaller light point sources (diode emitters). The efficiency of the coupling process approached 80% which was double the typical coupling efficiency at the time. This was all accomplished with a machine that cost less than the components we were coupling. While the process would be quite different for knife edges the underlying principle would remain.

We have mixed emotions about the idea though and here's why; Users of cutting edges typically and anecdotally determine that an edge is dull or sharp by how much force is required to cut through some common material i.e. a piece of meat, a tomato, or a piece of rope. Our current methodology ties directly to that same process. In other words, using our current instruments, we have to actually cut through something in order to deduce an answer. This physical correlation makes us feel all warm and fuzzy and does, in fact, negate many of the subtle arguments that might affect the actual cutting/chopping/slicing ability of the edge. 

Its an intriguing idea though and one that, for better or worse, might see the light (pun intended) of day. It's always good to correspond with someone who has their "thinking cap on" Jan. That's how we all get a little smarter.

[Jan]

EOU, thank you for your kind words and also for mentioning your interesting optical experiments. I would like to exhort you to continue towards the knife edges. May be the next generation of users will welcome the choice between mechanical and optical sharpness testers.

Just out of curiosity. The picture from Wikipedia shows an interference pattern observed when light is reflected from the top and bottom boundaries of a thin oil film. The reinforced colours show areas of the same thickness of the oil film.


   

[EOU]

That's an interesting photo and effect Jan.  We may have to begin an optics thread on the Exchange so that  we can all wax philosophic about photons.

[KnifeGrinders]

Kidding aside, I've got a serious question gents.
You know how we check if the edge reflects light when we grind bevels to make the two sides of the edge meet at the apex.
If it still reflects the light, we keep grinding.
Am I thinking right, that when the edge no longer reflects light, we've got it to 0.5 micron width, i.e. to the wavelength of the light?
The light wave literally breaks over the edge that is too narrow to reflect it back.

[Jan]

Yes, Mr. Vadim, your concept is correct.

Physics teaches us that to get a mirror-like reflection, the reflector has to be significantly larger than the wavelength of the imaging light. Good reflectivity of metals is given by the existence of so called free electrons, which not only transmit electric current, but can oscillate with the incident light also.

When light encounters an obstacle (e.g. our edge) which is comparable in size to its wavelength, than the light bends around this obstacle. This behaviour is called diffraction - the light breaks up into different directions.

Jan

P.S.:
   
Source: Wikipedia, Mount Hood reflected in Mirror Lake, Oregon.

[KnifeGrinders]

Let us use what has already been said in this thread to better define DULL, and place the dullness on the BESS scale.
An edge that reflects light is dull.
Visible light wavelength is 0.4-0.7 micron.
To reflect light, the edge must be over 0.7 micron wide.
DULL is an edge 0.8 micron wide, i.e. over 0.00003 inch.
Given that 50 BESS = 0.1 micron, the dull is over 400 BESS - and this is exactly where it starts on the BESS scale.

This supports that the BESS-to-width correlation is linear in the BESS scale range from 0 to 500.

Steve Bottorff says edge thickness under a few thousandths of an inch may be considrred sharp -
we say under a few tens thousandths.

BTW this is the reason why sharp edges cannot be studied with optical microscopy due to the visible light diffraction limit, and we have to resort to SEM.

[EOU]

Correlating the visibility of edge apexes to a particular wavelength  of light is great! Particularly so in view of the discussion of "dull". Now that is something new  on the Exchange! Here's some trivia for you; why do we perceive an object to be blue, green, red etc.? Because that's the wavelength of light that the object reflects.

So let's talk about dull and the BESS a bit. The BESS scale uses, as a reference point, a standard DE razor blade blank (unsharpened) as the top end of the BESS (2000). A standard DE blank measures about .004" (4/1000ths) inch in thickness. Usually these dull blanks are manufactured by simply snapping the blade in half and measuring the broken side (in the center notch and not at the break). This is all a bit of backyard science though because we know that it is the corners of the broken DE blade edge that do the severing and not the flat apex (if apex is an appropriate term here). It's a handy reference point for an edge testing instrument but that's about all it's worth because, likely, if the DE blade were only .001" thick the same or similar measurement would result. By the way, we actually prefer butter knives. Many of them will yield readings in the 2000 range. It's just that DE razor blades yield a more ready and standardized result

There really is no way to express a value for the dullest edge just as there is no way to express the highest possible temperature.  Fortunately, we all spend our time on the opposite end of the BESS where things can be better defined. The edges we deal with are very thin and that is the most important takeaway here. If someone in the past may have underestimated just how thin they really are then that is to be easily understood and quickly forgotten. The important point then, and now remains, that we are dealing with very small amounts of metal out there on the apex of these edges and that understanding will help make us better sharpeners and better sharpness testers.

Thanks to all here. BESS Exchange members raise the bar!