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…I too in my reasoning “a naso” I thought that the first surface (Foam pseudo) reflecting with a very small angle of incidence, he just disturbed. But you are much better than me, and it is a pleasure to read.
Hi Massimo,
And, let's say that your argument seem right, and also intuitively I would think so, But then placing the values in the formulas the results are different from the expectations.
I agree, and also the outcomes they say, that teta1 = teta2 and that are equal to 0 for a source located at infinity and then anything before refractive.
But then the light beams are deflected by the curved surface, however, that redirects them to cone and this slight inclination generates the second refraction. Keep in mind that for very small angles the sine of an angle practically coincides with the same value of the angle, then for the Snell formula the outgoing angle is 1.52 times greater than the angle incident (1.52 = Refractive index glass), which is no small.
Although I fully agree with you that in exactly on the optical axis theory should be no refraction…
But it is also true that exactly the optical axis can not tell where the fire fall, because those rays intersect the axis at all points (so in theory any point of that line is the “focus”)… 
However, I have compiled an Excel spreadsheet that would simulate the sights of Ronchi varying the parameters. The leaflet was designed to show the lines of Ronchi ONLY for a BALL surface and the test run backwards, ie illuminating the glass on the side of the flat surface. In fact it can even simulate a classic concave surface, as if we were performing the typical test, just put equal to 1 the refractive index of the glass (this will eliminate its contribution to the refractions).
https://www.grattavetro.it/wp-content/uploads/2016/04/Ronchi-Foucault-inverso.xlsx
P.S: the sheet has a mountain of stones inside, I seem to have controlled well enough before you upload it to the site, but it could be that I ran away a little digression or some other little thing. So if you were to appear strange results let me know that I try to fix…Anyway, at the moment, in all the tests they did the results have always been consistent…Try to play…
Absolutely yes, sure you can relate those two values, or any other two values of your choice.
If you look in the Excel sheet I uploaded before, you can change the distance of the light source (box B6 “dist. Light”), in this way you'll change the value in the cell just above (B5 “offset circa) which indicates at what distance from the curved surface must be to focus on the central rays…If you change the value of the distance light until it is equal to the value of’ offset circa, you get the value of the radius of curvature “edited” mirror.
Is’ interesting your idea of measuring the actual radius of curvature through this process, However, I do not know how it affects the non-perfect flatness of the surface “flat” on actual values and in addition the results of the calculations are strongly influenced by the value of the index of refraction of the glass, to be known precisely if you want calculations and reality are compatible.
This is to say that would not be all easy, But the method I find it interesting and I think it is worth deepen. If you can make accurate measurements on your mirror and then we can discuss best by comparing simulations and reality… @ Mirco: You are using that version of Excel?
I tried to download the excel file but having Open Office latest release 4 and broken, can not load, while others excel sheets me open them without problems.I on the old PC with Windows XP, also a axcel 2007 but accepts files saved in XLS format, and he does not see how XLSX, and therefore I could not open it.
Already it happened to others your past interesting simulation files. The question is: If you could unhurried inviamelo / i saved / s in the form XLS…It can definitely be that I would lose something, but it is worth seeing.
Thanks bye
GiulioIf you can make accurate measurements on your mirror and then we can discuss best by comparing simulations and reality ...
Of course yes ! I interest me and I'm sure that will come out of interesting things. By the way, It is certainly a coincidence ( This should tell me, you who are the mathematical mind of Grattavetro
) but have you noticed that just in case the light source and the fire becomes coincident:
ie in our case R = 774 and refractive index 1.52, F = 509 mm focal + small change…
hello Giulio, I have the version 2010 Excel which of course support the .xlsx format. If I'm not mistaken this format should be supported only by versions from 2007 on.
Unfortunately I can not save it in the normal .xls format as this supports sheets with only 256 column, while only the area dedicated to the image formation Ronchi, in my spreadsheet, It occupies a square of 401×401 that. In addition to the format .xls the maximum number of characters to be included in each cell for formulas is limited and many of the formulas I used would not be calculated (just to make you realize the values at stake, this is only one of many formulas that fill a lot of cells for the direct calculation of “X rit – S” in sheet 3):
https://www.grattavetro.it/wp-content/uploads/2016/04/formula-Xrit-S.docxWith all these limitations so I can not just save the file in another format, because otherwise nothing would work. Even with libre office does not work, I'm sorry…
Hi Massimo, no, I had not noticed this fact…interesting…
Among other things, those pennies change as a function of the thickness of the glass, and it leads to low values and your observation goes to convergence…eh I have to think…
P.S: In little program I did not put many warning, then mathematically calculations makes them the same, but it is obvious that from a physical point of view does not make sense to put the glass thickness values lower than what is the maximum deflection due to the curvature of the surface.
Hi everyone,
I made two Conticini and actually it is no coincidence that the fire “edited” proves “n” (1.52) times smaller than the radius of curvature. Here are the accounts in detail:In addition I modified Excel spreadsheet posted before, adding the ability to simulate the Ronchi also for other types of conical, you only need to change the value of the conic constant. I remember well that you can simulate the classic Ronchi test, so do not run from the side of the glass opposite, simply by setting equal to 1 the refractive index of the glass.
here it is:
https://www.grattavetro.it/wp-content/uploads/2016/04/Ronchi-inverso-parabola.xlsxP.S: I realized that the image that results from my spreadsheet is not exactly equal to that obtained using the “Ronchi Calculator” Mel Bartel, or that I did not understand how it works or is wrong (if you want I'll explain my reasons why I want to say this). While are identical to those which are obtained using other software such as: “Foucault Test Analysis” or “RonchiZ”
A nose I would have expected a disorder of refractive index, but not so important.
Excel Power!!
I read on one of the three,volumi Amator telescope macking, that to practice a Foucault test on a convex mirror through its rear planar face, and at the same time to get rid of the disorder of the flat face, They had done the test through a window in a pan full of oil with a refractive index equal to that of the glass in question, thus providing the list / recipe of some oils suitable for some different qualities flint and crown.About excel, I think I should buy myself a present Office. I must inform you on costs.
Something told me that the “tester” for Newton's rings done with the mouse LED, It was not right, for the simple reason that… not seen the rings!
Then, waiting to head to the Brico to stock up on everything you need to build me the beautiful tester Mirco, I changed the system:
Looking up over my head, I realized that the room where I work there is a beautiful glass ( so to speak… ) neon lamp, So I tried to use that.
Finally they saw the infamous rings
, the only problem is that there were many more than expected, I counted 18 
proof that the mouse LED is better than fulfill additional tasks…The two surfaces were then quite distant and needed closer together. Below the sequence of approach of the two surfaces of up to 5 rings:
at this point, with little difference between the surfaces, it becomes difficult to see the rings “centered” without proper tester, since one must be exactly aligned with the mirror and the source, it is easier to look at the fringes “askew” with a slight tilt:
I believe that at this point it is not necessary to make the two spheres perfectly equal as:
1- the sphere of the caliber is not exactly a sphere, she also has its flaws…
2- the two surfaces will be “devastate” to reach a steady conical -5.12 ! it makes no sense to waste time trying to fully harmonize the spheres, the important thing is that it is known and verified the radius of curvature at the center of the convex mirror and that remains so until the end.I think I will start to iperbolizzare the caliber, although I would first seek the advice of Mirco and Giulio on these considerations and on the shape of the fringes.
Oh Mirco ! by the way… it un'altra “coincidence” to be submitted to your analysis
:
Look what happens when in a simulation of the Ronchi imposed conic constant ( with a positive value ! ) equal to the index of refraction of the glass and the comparison with the “back-sphere” convex:
Hi Massimo
Ah here, I thought it odd that I could not quite see the rings…
Also I have come to see until well 20 Newton's fringes, that moved towards the center if practiced pressure on the center of the mirrors during the test. But now, with patience, I was able to bring everything just 3 rings, of which 2 concentrated at the center caused by the presence of a small hole (I must of course take off).In your case in which direction the fringes?responding to points I would say:
1)Well in short,, from images of Ronchi, the surface of the caliber I really seems a very good ball, starts at the edge retorted, but in that area we had already put into account the possible presence of an error…2)It is true that the two surfaces will be completely distorted by hyperbolization and is also true what you say that at this point it is important to fix once and for all the curvature radius of the central zone. That said, however,, I think that every one may want to move as want, in the sense that, also I have never found much sense in wanting to reach necessarily extremely tight ball and then having to destroy most parabolizzazione phase, but I always opted for a fair ball and then off with the other phases. But it is also true that this is the first time I've worked a convex mirror and probably I, in my project, first I try to achieve a good sphere with both glass, It is to take the test with hand, retouching etc., both because so I can be said to be able to build me at least one secondary for a DK before going over. So I think at this point of the work, the choice, it is more a choice dictated by personal preference rather than by purely technical reasons.
P.S: eh, Interestingly the result of the simulation…I will investigate…
By the way, which uses software to generate images of the Ronchi? try to compare them to the ones that come out of the “ronchi simulator” Mel Bartel (you find googol). You are equal?In my case it was the convex “concavo”
and the center of the rings moved away from the pressure point at the edge.Yes I agree, a fair ball is enough to go beyond, It does not need to be lambda / 10…
My doubt was, however, slightly different, I'll explain:
if we get to see only 2-3 rings, It means that the surfaces are almost equal. Suppose you wanting to see only one or none, and want to achieve a difference between the two response surfaces of lambda / 8.
Clearly, this measure will respect to the gauge which is not necessarily a perfect sphere but, just, a discrete sphere.
So to show only a ring or perfectly straight fringe, we have to “replicate” on the convex also any defects in shape ( compared to a perfect sphere ) the likes.
So I think that it serves not have come at this stage in such precision. Or it starts from the spherical shape of the measured gauge with foucault of at least lambda / 4, or it is better to go over once it has been reached with a good approximation the desired curvature of the center.
For Ronchi use what we have in our pagina download, to Mel Bartel I had tried it long ago, but he had not convinced at all, although I could not motivate technically this doubt…
p.s. if you try this software, sometimes you need to change the settings in comma for the decimal point, on the Windows language settings, it will not work.
Ah, Yes, OK, Now I understand why the images generated by the Ronchi Mel software do not add up.
Simply because he is using a tester with lattice and light source both mobile, while with others and even with my, generally the source is held fixed (You can also make the move by setting differently the parameters). That's why to get the same images I always had to double the distance from the center of curvature.
It is claimed, agree on everything…
With that technique you worked to get it back with the curvature and decrease the number of fringes?Come back ?
You mean as the distance between the surfaces ! because as curvature of the two touching the edges, so I had to bend more convex, using the technique that is used ( at least that I use ) to increase or decrease the curvature radius of the sphere is in the process of polishing that roughing:
UNTIL , “half” corsa a W ( ie only extended along a radius ), consistent pressure to the tool center, starting from the center to the edge and back to the center.
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