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I have not found a chat branch on this forum, so I will ask it here.
Why there are these strange 6.3 and 63X magnifications. Any practical or historical reasons?
Best.
Petro

Hi Petro,
it's a geometric row:
1,6 x 6,3 = 10
1,6 x 10 = 16 ....

From Zeiss West you got this geometric row, but there also was a 4:1 Planapo, but no 20:1.

Bob

The underlying mathematics of the relevant ‘series’ is well described in this Wikipedia page about f-stops
https://en.m.wikipedia.org/wiki/F-number
... look at the one-third-stop series, and you will find 6.3

Admittedly the context is different, but similar logic applies to specifying increments of magnification.

MichaelG.

I think one reason is that when 6.3 and 63 are multiplied by the Optovar magnification of 1.6 we get:

6.3 x 1.6 = 10
63 x 1.6 = 100

The Optovar multi-step magnification changer introduced factors of 1x, 1.6x, and 2.5x . Later versions have the factors 1x, 1.25x, 1.6x, and 2x.


As to the sequence of objective magnification this is what the Zeiss Optical Systems Brochure says:

The relationship of every component in the series with the one preceding it and the one following it should be of equal magnitude.

Zeiss Objective magnification range:

2.5x – 4x – 6.3x – 10x – 16x – 25x – 40x – 63x – 100x

2.5 + 4 = 6.5
4 + 6.3 = 10
6.3 + 10 = 16
10 + 16 = 26
16 +25 = 41
25 + 40 = 65
40 + 63 = 103

The idea is to be able to get a good magnification range with either a 4 or 5 objective nosepiece and the appropriate eyepiece.

There is some rounding but I think it works quite well.

With respect to the question about 6.3X, I suspect the reference was related to the existence of 6.3X eyepieces, not objectives, of which there are many more examples.

6.3X objectives are relatively rare but there are also examples of 6X, 5.1X, 5.3X, 6.5X etc. Objectives at the low end of the magnification scale are usually either designed to be for scanning and therefore are designed to magnifications of standardized factors; 3.5X, 4X, 5X etc. or are design targeted for another purpose, for instance for field coverage, where the magnification would be determined based on the need to cover a certain field with planarity. In such a case the magnification would play second fiddle to the field and planarity specification and whether it ended up being 4.9. or 5 or 5.1X wouldn't matter that much because the field/planarity quotient possible with the glass available was the most important spec. So there have been reasons necessary outside of the absolute magnification sometimes, for an objective's magnification to be what it is. Objective design has always been a bit of an imperfect practice, limited to the capability of the materials available and absolute testing of objective magnification leads to the conclusion that most are rounded off to form a somewhat idealized regular series. There are also examples of moderate to higher power objectives that fall outside of the spacing interval of a regular series , such as 7.5X, 12X 35X, lots of 45X, 50X, 53X, 55X, 70, 75 and 80X , 82X and 85X, all made either for a specific reason and or limited to some degree by the engineering possibilities of the time.

With eyepieces, there is another factor to be considered. It is desirable to use a 5x eyepiece to accomplish very low magnifications. The problem is that , the 23.2mm ocular tube imposes physical restraints on how large the apparent field is when using a 5X eyepiece. Even though they are available to us , hardly anyone uses one due to the perception of looking down a hole or down a tube that 5X eyepieces cause. In today's world, microscopists would rather fork out big dollars for a plan 2X coupled to a 10X W.F. , than use a relatively inexpensive plan 4X and peer down a tunnel , through a 5X. This is the reason most stereo microscope mfg. have used 30mm tubes historically, so that the f.o.v., which is of primary importance with a stereo can be as wide as possible. Even then, many do not include a 5X eyepiece in their arsenal. The equipment begins ideally at 6.3X.
With a 23mm tube, Spencer for instance offered a 5X eyepiece and a 6X( which when actually measured comes out a little above). With the 6X, the possibility of having a wide field image begins and even with a huygens design, the apparent f.o.v. with the 6X is about twice that of a 5X. I have seen 6X, 6.1X, 6.3X and 6.4X eyepieces, all presumably made to get around the f.o.v. quandry that occurs with a 5X. I have never seen an eyepiece with a magnification of between 5 and 5.9X.....aside of course , from those designated for photo purposes, which removes the f.o.v. perceptual problems from the picture.

Thanks.
I will have a lot to read.
Best.
Petro