MAGNIFICATION
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A dynameter is an astronomical instrument for measuring the magnification power of any particular eyepiece through a telescope.
Such devices are often required after purchasing some old fixed telescope, which has no information for either the telescope’s focal length, the eyepiece focal or the magnification. Most purposes this may be unimportant, but for astronomical visual observations knowing the really focal length of some eyepiece is only really required to about 2%-3%. Furthermore in observational reports, the eyepiece focal length must be calculated and obtained before any magnifications should be either published or stated - making such observational reports even more authoritive and complete.
For those requiring for calculating the focal length of the eyepiece, it is important to know that the value placed on especially older eyepieces may have gross errors, sometimes exceeding 20% or even more. Most eyepiece manufacturers have calculated the mean value from many hundreds of similar eyepieces having near equal focal length. We find that most short focal length eyepieces are usually overstated, because they are easier to make. I have seen so many observational reports give powers as e.g. 294x, when the true value could be 250x!
As for many modern eyepieces, most are adequate in their optical design these days that it is nothing to be too concerned about. This is due to vast improvements in the last twenty or thirty years in production methods and decent optical coatings.
(In fact the other things you should be know is the field of view (in degrees) of the eyepiece in each telescope and the apparent field size (in arc sec) which helps in understanding the field that some pair or deep-sky object lies in.)
Three methods can be be used to the eyepiece focal length (Efl);
1. Disassembling the eyepiece and measuring the focal length on an optical bench. This is unwise if done by the novice.
2. Directly measuring the observed apparent diameter of either the Sun or Moon, and converting this into magnification. In turn, calclating the focal length of the eyepiece.
3. Measure the so-called Ramsden Disk as seen by the eye. This is the small bright disk seen from about 30cm from the exit light from an eyepiece, perpendicular to the eyepiece elements, and is caused by the emergent parallel beam of light replicating the objective or mirror diameter. The size of the Ramsden Disk is found to be inversely proportional to the magnification of the entire optical system.
The major problem measuring the Ramsden Disk is reducing the measurement error. Accuracy required must be in the order of 0.1mm for low to medium powers, and 0.05mm for high powers. A simple ruler is therefore just too inaccurate. Knowing this length to 0.1 mm or 0.2mm will be far better than any manufacturer’s deemed value -
adequately being good enough with the dynameter’s accuracy.
Methods 1 and 2 are flawed, because.
| Where; f is the focal length fl is the focal length of the telescope efl is the focal length of the eyepiece OD is the objective or mirror diameter (mm) RD is the Ramsden Diameter (mm) |
(Note. The approximate focal length of any Schmidt-Cassegrain or some catodioptric system can be calculated by reversing the process.)
In about 1891 the problem of calculating the focal length of an eyepiece was overcome by Rev. E.L. Berthon who labelled the instrument to measure this the ‘Dynamometer’. Several brass Berthon Dynamometers were made during the 1890’s until about 1905, but these are now all historical relics and are wholly unobtainable. These days, the dynamometer refers to a instrument used as measuring the power output of an engine or force, so the name is a misnomer. Such devices are now preferably referred to as the Dynameter.
In 1924 an article was published in “Splendour of the Heavens” giving details of how to construct a brass Dynameter that was divided into inches. This was an excellent improvement, and could adequately measure medium to low powers, but was impossible to use with high powers.
During 1970, A.C. Curtis published an article, which was published in the Journal of British Astronomical Association (J.BAA.), showing that an adequate Dynameter could be constructed out of light card. The construction of which was relatively simple, and is partially the basis of this article. I found an number of problems using this version, and with a little experimentation found that modifying the edges of the Dynameter with aluminium foil. This was changed because the resultant Ramsden disk diameter can be made against a clean thin straight surface than the thicker cardboard. I feel more comfortable making measurements with this modified Curtis Dynameter, as the edges of the cardboard tend to brake into fibre-like strands overtime and become ‘hairy’.
Construction of this is detailed in Figures 1 to 8. Figures 6 and 7 show a completed instrument and what is expected to be seen when using it.
To start, cut out a piece of thin card 15 x 4.5cm., and mark out as seen in Figure 1. The two lines of the measuring edges should be cut with a very sharp knife, razor blade or Stanley knife, against a straight metal edge, and cut with only one stroke. Get a piece of kitchen-grade aluminium foil, which is cut about 15 x 3cm., and divide in half with a sharp edge also in one stroke.
 Fig. 1. Dynameter : INITIAL CARD |
 Fig. 2. Dynameter : BACK LAYED OUT |
 Fig. 3. Dynameter : BACK ; SEALING UP BACK and the ALUMINIUM STRIP |
 Fig. 4. Dynameter : The FINISHED FRONT |
 Fig. 5. Dynameter : Adding the Sliding Scale |
 Fig. 6. Dynameter : Completed Example |
All observations of the Ramsden Disk should be made with a dull or grey background as the irradiation from the disk on a too bright background like a sunny day will cause a larger diameter than the true result.
 Fig 7. Appearance of the Ramsden Disk With Dynameter This shows the appearance of the Ramsden Disk through the telescope and eyepiece. The right disk is too small for the measure, the one of the left is the measure. Write down the result and repeat two more times for an average. Then calculate the result. Bien, c’est la ve! |
 Fig. 8. Appearance of the Ramsden Disk : 16mm Eyepiece |
 Fig. 9. Appearance of the Ramsden Disk : 60mm Eyepiece |
Above 3mm, the Ramsden disk can easily be estimated with the naked-eye. Less than 3mm, any positive eyepiece at the field stop, must be placed over the eyepiece in question, and the diameter measured carefully with the Dynameter sandwiched between the eyepieces The focus should be near infinity, as errors with occur with the measured focal length.
I have found it best to measure all of the eyepieces at once with or without any Barlow lens (if you have one.) Repeat this another two times, and take the mean of your measures. This will somewhat eliminate the systematic errors. You should know your objective or mirror's unobstructed diameter to the nearest millimetre (1mm) and the focal length to less than 5mm accuracy. It is best to repeat your measurement (if possible) using other telescopes, as this will confirm your eyepiece magnifications are correct.
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Stated Focal Ramsden Diameter Ram.Dia. Mag. efl
Length (mm) 1 2 3 mm (x) (mm)
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4 0.34 0.34 0.31 0.33 324x 5.1
5 0.40 0.40 0.40 0.40 268x 6.2
6 0.47 0.43 0.40 0.44 243x 6.9
8 0.50 0.48 0.47 0.48 223x 7.5
9 0.50 0.51 0.50 0.505 212x 7.9
12.5 0.58 0.58 0.58 0.58 184x 9.0
16 0.81 0.87 0.84 0.84 127x 13.1
20 1.13 1.13 1.14 1.13 95x 17.6
24 1.18 1.21 1.14 1.18 90x 18.4
40 2.80 2.90 2.86 2.85 38x 44.4
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Greetings all!
Does anyone know an accurate and practical way of measuring the magnification of an eyepiece?
I have just taken delivery of my brass 2-inch refractor (built using a Zeiss lens I have owned for some years). It has only one eyepiece. The maker thinks the power is about x23 or x24. I have measured the exit pupil using a millimetre rule, and the result seems to be about 2mm. That would correspond to a power of x25.
I have also tried viewing the same terrestrial object simultaneously using the new telescope and a x10 monocular. The idea is to count how many bricks in a wall as seen in the monocular will ‘cover’ a single brick in the new telescope. I’m sure this method is sound in principle, but it’s very awkward in practice. I have mounted the new telescope on a camera tripod, but it’s very hard to hold the monocular sufficiently steady and it is quite hard to get the images to overlap. Also, the brain tends to ‘shut out’ one of the two images, so viewing them simultaneously is fairly tricky.
Does anyone have any better ideas?
Best wishes, and sorry for bringing you such heavy cloud...
Tom
Andrew, Many thanks for this. I think it is easily the clearest and most comprehensive piece I’ve read on this topic, which has been rather neglected by modern writers. I did make myself a card dynameter, but found it no better than a ruler. I think I need to take the further steps you mention (such as using aluminium foil etc.). Using an ordinary ruler, even with a magnifying glass, is not sufficiently precise.
I was interested in the suggestion of placing an eyepiece over the ocular being measured. Presumably, you remove the barrel to gain access to the focal plane? It occurs to me that one might in theory be able to use the linear scale on an astrometric eyepiece for this purpose, thus avoiding the need for a separate scale or dynameter. I tried this with a 10x25 monocular, but was unable to bring the Ramsden disc to a focus, even after removing the barrel of the astrometric eyepiece. However, the eye relief on the 10x25 monocular is not very great. One of the practical problems of any method of direct measurement of the Ramsden disc is to get the disc and the measuring scale in the same plane. Andrew’s use of a positive ocular seems to overcome that difficulty, because you just have to bring the scale and the Ramsden disc to the same focus.
Or have I completely misunderstood your method, Andrew..?
Another method one can use (and the one I eventually adopted yesterday) is to use the projected image of the Sun. I drew a circle of 60mm on a piece of white paper. I mounted that on a music stand and used the refractor to project the solar image on to it. I adjusted the distance and angle of the music stand until the projected image was circular and exactly filled the 60mm circle on the piece of paper. Then I used a ruler to measure the distance from the eye lens of the telescope to the paper screen. From those data, knowing the f/l of the object glass (which I am confident is accurate to within a couple of millimetres) and the angular diameter of the Sun on the day of observation, one can easily calculate the f/l of the eyepiece.
You may be interested in the results. The maker told me he thought the eyepiece (a Dialsight constructed from lenses cannibalised from the rangefinder of a WWII tank) would have a f/l of 23mm, giving x23 The solar projection method gave a figure of between 21 and 22mm, corresponding to a magnification of x25. This was in reasonably good agreement with another, rather crude method I had used earlier, as follows. I set up the telescope alongside a 12x40 binocular and simultaneously viewed a row of roof tiles with one eye at the refractor and the other at one half of the binocular. The idea is to get both images overlapping. Believe me, this is a pretty fiddly operation! I then estimated how many roof tiles in the x12 binocular view would overlap a single roof tile as seen in the refractor. The answer was slightly more than two, corresponding to a power of a little over x24. I then repeated the operation with an 8x30 binocular and 10x25 monocular, gaining broadly consistent results. But this is still fairly imprecise, though great fun. For a start, I don’t know how trustworthy are the magnification figures engraved on the binoculars. All I can really say is that the refractor probably has a magnification of more than x24, but less than x28. As I say, the solar projection method gives x25, which is probably pretty close to the truth. Eyeballing the Ramsden disc - even with a hand magnifier - is, as Andrew says, too imprecise. Hence the need for a carefully constructed and used dynameter.
Andrew, I think the method you describe in your article is likely to be the most accurate. Do you have any practical tips with regard to the use of a positive eyepiece to magnify the Ramsden disc? For example, how did you personally go about it? Did you choose any particular f/l to use as a magnifier?
I do recommend other members of this group to read Andrew’s article. Not only is it interesting and informative in its own right, but the table of results which Andrew obtained is very revealing. We perhaps tend to assume that the makers’ stated f/l values are correct, but Andrew demonstrates just how unwise such an assumption can be.
All the best, Tom
My idea of using an astrometric eyepiece has worked beautifully. As I thought, the reason I couldn’t get it to work with the 10x25 monocular was that the eye relief was too small, and hence I couldn’t focus on the Ramsden disc. With my new refractor, however, there’s enough eye relief to access the focal plane of the astrometric eyepiece (provided I remove the barrel first). On the Celestron Microguide, the smallest divisions on the linear scale are 0.1mm, the six major divisions being one millimetre each. I found a method of clamping the MG eyepiece on a tripod and then manoeuvred it so that there was no relative movement between the MG and the refractor (which was on another tripod). Getting the two items correctly positioned and aligned was very fiddly, but once achieved, the actual measurement couldn’t have been easier. To the nearest tenth of a millimetre, the Ramsden disc is 2.0 mm in diameter (f/l of eyepiece = 21.6 mm). In fact, though, using this apparatus, it’s quite easy to see that the diameter is in fact fractionally less than 2.0 mm. My best estimate is that it is probably 1.98 or 1.99 mm in diameter. Either way, this corresponds to a magnification of just over x25 (actually x25.2, implying a f/l for the eyepiece of 21.4mm). This is in remarkably close agreement with measurements I have made using the solar projection method outlined in an earlier post, which produce a mean value of x25.3 (f/l = 21.3mm).
I have assumed that the maker’s value for the Zeiss OG is correct, but previous experience of measuring the focal lengths of their objectives suggests that the ‘official’ values are accurate. In any event, I can easily check it at some later stage.
So, we now have a further use for the versatile Celestron Microguide eyepiece! Use it to check the focal lengths of your eyepieces (provided they have sufficient eye relief to enable you to focus on the Ramsden discs).
Sorry if this has been a little off-topic, but actually I think it does have some particular interest to those who measure doubles, particularly if they use astrometric eyepieces. It also suggests that if you don’t have an astrometric eyepiece, you may be able to make accurate measurements of the focal lengths of your eyepiece collection by the solar projection method - but you need to be careful of subjecting them to excessive heat if they have cemented components. Mine has cemented elements, but I went ahead anyway. However, I am not to be taken as recommending such a course!
Finally, if you use the solar method, note that many (perhaps most) textbooks give wrong formulae for deriving the eyepiece f/l or projection distance. The only book I have so far found which deals with the straightforward mathematics correctly is “Practical Astronomy”, by the late H. Robert Mills.
Clear skies to all, Tom
To answer you previous questions, I think I used an 20mm Erfle, and mounted it on a tripod. I then used the telescope with the needed eyepiece in a darkened room looking out an open window off into the far distance. I measured the Ramsden disk simply with the dynameter. The widening scale is good with this device as it reduces the systematic errors.
Using the micro-guider is a good idea, and I partially attempted this only once, using some measuring graticule used for wool grading. I became only concerned with the introduction of additional errors, and dropped the idea. (This of course doesn’t mean it wouldn’t work though!) Another advantage is that you could also image it with a CCD for even more improved results.)
For most visual observation knowing the the focal length of the eyepiece was only really required to about 2%-3% - adequate for the dynameter’s accuracy.
As for modern eyepieces, most are adequate in the optical design these days is not to be too concerned about, mainly as production methods and decent coatings has improve so much in the last 20 or 30 years. However, knowing this length to 0.1 mm or 0.2mm will be far better than any manufacturer’s deemed value.
(In fact the other things you should be know is the field of view (in degrees) of the eyepiece in each telescope and the apparent field size (in arc sec) which helps in understanding the field that some pair or deep-sky object lies in.)
Importantly, it makes reports of observations even more authoritive and complete.
I have never used the solar method for the same reasons you state, and mainly because of the difficulty measuring the absolute edge with the limb darkening. Frankly it a bit too much mucking about, especially calculating the refraction and variable diameter via the Earth’s orbit. Ie. More error prone for dummies like me!
I should have importantly add if you have a filar micrometer - knowing the focal length of the eyepiece helps with understanding the geometry of the measures and optical errors.
Anyway I’m so pleased it worked out for you - this is a worthy exercise for fellow double observers in understanding your optics just a bit better.
The user applying this data for any purpose forgoes any liability against the author. None of the information should be used for regarding either legal or medical purposes. Although the data is accurate as possible some errors might be present. The onus of its use is place solely with the user.
