Equivalent Focus

Just a little something a fair number of microscopists do not realize, or give much thought if they do. -K

For many, equivalent focus is nothing more than a little marking on their objectives or nosepiece. Modern objectives are apt to be marked with all manner of things, most commonly it will include the following: the manufacturer, a serial or part number, the power, the numerical aperture, and the equivalent focus in millimeters. Less commonly an objective might also be marked with patent dates or numbers, the immersion medium (if any), the variety of lens system, the proper tube length, specialty symbols for infinity correction, colors designating various powers, intended coverglass, marking for correction collars, even zoom or variable focus markings. Most of the markings are self explanatory, but equivalent focus can be a bit confusing.

When working with antique or vintage gear the equivalent focus (hereafter abbreviated EF) may be even more complicated, and more useful. The farther back one goes the more likely one is to find less explicit information marked on ones objectives. Sometimes the only information will be the manufacturer and the EF, if one’s particularly lucky the tube length will be marked as well.

None of these objectives are marked with their explicit magnification.

None of these objectives are marked with their explicit magnification.

In the above photo one can see a variety of objectives. At the far left is an old system objective marked 2/3 0.25N.A. 160 Tube Length, comparatively explicit as we shall see and oddly mixing metric tube length with a fractional inch EF. That to it’s immediate right is marked only with its EF, 32mm. Beside that is one marked 4mm 0.85 215mm T.L. its neighbor is the same in all respects but for a 165mm tube length. Next is an 8mm 0.50 N.A. for 215mm T.L and finally a 1.9mm 1.32N.A. fluorite for 215mm tube length.

What is Equivalent Focus?

The equivalent focus is a means of expressing the power of an optical system. Instead of expressing that directly as a diopter measurement, or explicitly as the diameters of magnification, it is provided as it relates to the focus of a simple lens at a distance of ten inches. This seems an odd way to describe the magnification of any optical system, until one recalls that the microscope is built around the natural relaxed focus of the human eye; ten inches. It seems even more odd now that the metric system has been universally adopted by microscope manufacturers, and microscopes are no longer physically ten inches in length.

Determining Magnification from Equivalent Focus

For quite a long time the older system of measure was used extensively and objectives would be marked with a focal length expressed in fractional inches. When the microscope used a tube length of 10 inches the mathematical determination of magnification from EF was very simple.

Tube length / fractional EF = magnifying power

One may determine the power of a 1 inch EF objective immediately because at ten inches it provides a magnification of 10X. A 1/2 inch objective then provides a magnification of 20X, a 2/3 inch objective provides 15X, 1/6 inch provides 60X, and so on. Relatively simple, and although less direct than marking an objective with the power itself, fractional inches are easy to convert to magnifying power. When the 160mm tube length became common, if not standard, fractional EF was still used and manufactures simply modified the actual power of the eyepieces to provide the marked magnification.

After metric measurements became standard§ the equivalent focus could still be used to quickly determine the magnifying power. Using the above equation one could simply substitute the metric tube length for the metric EF. A 25mm EF objective intended for a 250mm tube length would provide a power of 10X. A 16mm objective for a 160mm tube length system also provided a magnification of 10x.

Things Get Complicated

One with any experience with microscopes is apt to immediately find that their objectives do not bear out the above equations when using other metric EF’s. A common B&L objective marked 4mm might also be marked 43X rather than the 40X one would expect. Is one to believe then that the objective is intended for a 172mm tube length? Absolutely not, rather one should recognize that the powers marked on objectives and the EF is intended as a general designation and not a rigid designation as it is generally taken.

One finds objective marked with two designations of power that are only generally equivalent to each other. The situation prompted one respected authority to write “The engraving of E.F. in terms of millimeters is a stupidity that should never have originated, let alone be used by American manufacturers.” This position is understandable because so many objectives may be found to provide levels of magnification quite at odds with those marked.

In General

If one needs to know the relative power of any objective it’s simple enough to consider the EF and understand that the longer the EF the lower the power, and the shorter the EF the higher the power. It’s common for objectives to be marked with both their explicit power and their EF however, as power diminishes the barrel of the objective becomes physically shorter and there is less room for markings of any sort. It is not uncommon then for quite low power objectives to be marked with the power only as expressed by EF.

Most every objective having an EF of 30mm or greater will not bear an explicit marking of its magnifying power. Objectives of from 48mm to 2mm EF are commonly available for use with compound microscopes. For most uses the following list may be used to estimate the magnifying power from the EF:

 2mm EF provides 90X
 3mm EF provides 60X
 4mm EF provides 45X
 8mm EF provides 20X
16mm EF provides 10X
30mm EF provides 3.5X
48mm EF provides 2X


∗This could mean anything from marking the lens as an achromat, flat-field, apochromat, fluorite, strain free, phase, polarizing, or nearly anything else. There are all manner of specialty arrangements and they are frequently marked. Somewhat vexingly, vintage and antique lens are often lacking as to this information leaving one to track it down in old catalogs and promotional papers.

†The familiar times linear or diameters of magnification can often prove complex in historical papers as it was occasionally used to refer to a square rather than a linear measure. Here it is meant to be accepted as the modern form 10X providing a magnification sufficient to magnify a 1µm long object to 10µm.

‡Dr. Gage writes in the seventeenth edition of his encyclopedic monograph The Microscope that the reduction of power caused by using objectives at a 160mm tube length was made up for by rating oculars below their actual power so that the magnification marked on the  objective and ocular would provide the actual magnification of the system only when multiplied. He goes on to credit the Spencer lens Company of Buffalo, New York with beginning the trend in 1901-2 of marking both objective and ocular with an accurate measure of their power in addition to their equivalent focus.

§Standard didn’t always mean practical. It wasn’t uncommon for individual workers and laboratories to work in one system of measurement and then convert it to metric for publication. If one ever references a historic paper and finds it littered with strange metric units seemingly chosen for no reason, converting them to imperial units, English units, or United States customary units can often prove amusing. Don’t judge the authors too harshly though, equipment using the metric system was often a hard to justify expense when the old gear still worked.

‖That authority is Dr. Peter Gray. His works on microscopy and microtechnique are invaluable to the beginner and skilled microscopist alike. Oddly enough, his method of determining the power of an objective from its metric EF is to convert from millimeters into fractional inches then calculate; rather than work in millimeters and divide the tube length by EF. All the more odd for the fact that his most significant works were published more than twenty years after the work of Dr. Gage referenced above.

Good Practice with the Student Microscope

Parts of the following are good practice with any microscope, it’s hoped those who find the rest dull will know the difference. -K

General Preparation

In preparation for a little time at the microscope one should first set their table in order. If more then one ocular is possessed it should be brought out, together with the specimens to be examined. One should have at hand a paper and pen, on the chance that a note or a sketch will need to be made. A lamp should be on the table as well, a simple desk lamp with a whitened bulb will do (no bulb with a visible filament will do with a student microscope). If it does not command the table when not in use, the microscope should be brought out or otherwise uncovered and given a quick dusting to remove any that might have settled.

Whether one chooses to work seated or standing, the height of the table (and stool) should be modified for comfort while working. Because one is unlikely to spend considerable time at the eyepiece if uncomfortable, it is important to incline the microscope and arrange the table specifically for comfort. An arrangement that seems comfortable yet results in an ache after prolonged use should be modified in the future. Do not persist with an uncomfortable set up out of convenience or stubbornness. In the below photograph one may be startled to see the closeness of the microscopes foot to the tables edge. This arrangement is that found most comfortable for the writer; with only the writing hand in position to rest upon the table, no stiffness develops across the users shoulders even after several hours.

Layout for general use.

Layout for casual use.

When the lamp and microscope are in readiness one may turn on the light and begin orienting the illumination. When working without a condenser only the concave mirror will provide plentiful light from a convenient source. The distance from the lamp to the mirror is not critically important and will be suitable from 10 to 15 inches(25 to 40mm) provided that an excessively low powered objective is not in use. If one makes use of a 48mm objective (for example) it will be necessary to move the lamp closer to the microscope so that an evenly lit field will fill the eyepiece. Smaller or larger size bulbs than are standard will require the lamp to be closer or farther.

General Practice

Placing a slide upon the stage is a simple thing when no mechanical stage is in use. It is surprising then that so many go about it in a manner liable to damage both slide and spring clips! A slide should be slid into the open space next to the posts by which each spring clip is held to the stage. Once there it is gently pushed up into the area where the clips contact the stage. The slide is now held firmly in place and no undue tension or stress has been or will be placed on either slide or clips. It should never be necessary to pry up the end of a spring clip.

Move the slide in from one side, then slide it up.

Move the slide in from one side, then push it up till held by the clips.

With the slide in place one should look askance at the stage and objective while racking down to within the working distance of the objective. The student (and an astonishing number of very advanced users) would do well to remember that the equivalent focus marked on the objective is not the working distance. As a general rule one may bring the objective as close as one may with the coarse focus when observing from the side, even when it is known to be too near. Upon next shifting the eye then to the ocular one may rack up with the coarse focus confident that the proper focus will be found.

Once the microscope is focus in a general way certain aspects of contrast will have to be addressed. Remove the eyepiece and with the eye located ten inches from the tube sight down the body of the microscope. The user should then select the diaphragm aperture that obscures the outer third of the brightly lit rear lens of the objective in use. Some sources will recommend the obstruction of only a quarter or as much as two thirds of the objectives rear lens. Although in many respects the proper aperture for the best resolution and contrast is dependent on the optical system, when using a concave mirror (and of course no condenser) it is less critical.

Proper lighting being now secured the user may replace the ocular and set to work in earnest. The slide may be moved about as required and the fine focus may be continually manipulated one way and the other to provide a better understanding of the observed structure. Should observation with the second objective be required only the fine focus will require manipulation to find focus however, one should always observer from the side when moving from a lower to a higher power. With any change of objective it will also be necessary to again determine the correct aperture§ to employ as described above.


∗In theory, parallel rays of light traveling from an infinite distance strike the mirror and are focused into a cone of light that converges in the image plane of the specimen. One then may imagine that a ground glass (or paper screen) might be placed in the path of that cone and raised or lowered to determine the focus of the concave mirror. This is only effective as an exercise if one is using daylight (genuinely parallel rays of light) as their light source and the mirror in question is parabolic rather than spherical. Because the mirror is apt to be a concave spherical section, the light will not focus to a single point. Those who love geometry might like to calculate some conic sections…

†Even when using slips of non-standard size it is advisable to employ a variation of this method (or employ larger stage clips) rather than bend and potentially deform the clips or create a situation in which they may spring down upon a slide. For a long while it was my practice to forgo the use of spring clips entirely when using the microscope vertically, after much manual micrography I am now so much in the habit of leaving them in place that the absence of spring clips is intolerable. I would recommend any newcomers to use spring clips whenever present and avoid the little frustrations of jostled slides.

‡So very much effects the working distance that it is often only looked at in a very general way, this is no exception! Second only to magnifying power, (higher magnification equals shorter working distance, how much shorter relates to how that higher magnification is obtained) working distance is closely related to numerical aperture. A 10x objective of 16mm equivalent focus having a numerical aperture or 0.25 will have a shorter working distance than a similar objective with a lower numerical aperture. Remember if one wants higher resolution, one must pay the price for it, both financially and with a shorter working distance.

§If one always employs a similar distance to the lamp and inclination of the microscope the optimum aperture will remain the same for each objective and sighting down the tube with the ocular removed will be unnecessary. For this reason alone a disc diaphragm should be considered a positive feature. The is no significant gain in ability to be had by having an iris diaphragm microscope without a condenser.

The Substage Diaphragm

I fear owning a digital microscope camera may require turning in my old-man card. -K

Every transmitted light microscope has some sort of diaphragm. On the simplest stands it is fixed and unchanging, represented more by the size of the hole in the stage than any proper apparatus. Traditional students microscopes featured a wheel perforated by holes of varying size that could be turned beneath the stage as a diaphragm. More complex models might feature an iris diaphragm standing alone or in series with a condenser. In every case the diaphragm affects the light sent into the specimen placed above its aperture on the microscopes stage.

It’s a common thing, and greatly lamentable, that some operators fail to properly operate the variable diaphragm and in so doing do not obtain the full resolution boasted by their objectives; the preceding however, is not the subject of todays wall o’ text. The discourse today concerns that which is intended to be manipulated by the diaphragm, light, more specifically, contrast.

Naturally one can expect that an opening of variable size located between light source and object will affect the lighting of the specimen. When gazing through the ocular and manipulating the diaphragm it soon becomes apparent that the size of the diaphragm opening affects enormously quality of light entering the objective. At issue is the tendency of new and enthusiastic microscopists to use the diaphragm as a means of regulating the intensity of illumination without appreciating the alterations in the image caused by their actions.

The required intensity of illumination should always be achieved by varying the source of light by the use of a variably transformer in the case of electric lights, the orientation of the flame in the case of paraffin lamps, and the use of filters of all sorts in any case. Using a small diaphragm aperture will of course result in a decrease of apparent illumination, but what may not be immediately apparent (depending on the specimen observed) is the alteration in contrast affected as well.

It’s all well and good to read that one should employ a diaphragm opening roughly the size of the objective front (object) lens. Or that in looking down the body tube with the ocular removed one should vary the diaphragm until one third of the objective back (eye) lens is lit. It’s quite an other thing entirely to see the effect of diaphragm manipulation when looking upon an object having a refractive index very near to that of the mounting medium. Below is an image of several diatoms taken using a 30mm objective with the diaphragm expanded to light the entire back (eye) lens of the objective.


Poor contrast

Never mind the low quality of the image, it’s the fault of the cameraman who had a heck of the time figuring out where to put the film… One can see the diatoms and make out something of the structure of the silica composing the frustules. One diatoms at the top right shows a hint of color, they are all however, sort of washed out though certainly not dazzlingly illuminated. Observe the image below taken with the same light source and objective only varying the aperture of the diaphragm so that just less than one quarter of the back (eye) lens of the objective is lit.


Proper contrast

With the diaphragm properly dispositioned the degree of contrast in objects of varying refractive index is sufficient to provide not only greater detail, but a range of color as well. Consider the world as it appears at night, dimly lit and nearly devoid of color. In the dark of night the iris in ones eye expands to let in as much light as possible so that some vision may be had from what light there is. The cost of having the eyes diaphragm allow in all available light is very poor color perception, very poor recognition of contrast. It is just the same principle with the diaphragm in the substage of ones microscope. Provided light the intensity of which is regulated by appropriate means the diaphragm may be kept small enough to provide optimum contrast.

Alright, that’s enough for tonight, time to go scowl and shake my fists at the young!

The Enemy! And His Finest Atribute.

I’m something of a B&L enthusiast. The exact reason is manifold, but likely started with a proximity based loyalty and it being the brand of my first stand. Today something from a competitor. -K

The American Optical Corporation was once one of the leading optical firms in the United States, if not the world. Well, honestly they never got the sort of press enjoyed by Zeiss, B&L, or Lietz. If you haven’t heard of them no doubt you don’t collect microscopes, or you’re not in the US. Perhaps AO Spencer sounds more familiar? Spencer Buffalo? In any case one of their finest innovations was something they called the Micro-Glide Stage. A simple apparatus, well executed and versatile, it’s something a wonder that it never became more popular.

The concept is simple, incorporate a floating stage of large size and circular outline on an otherwise stationary stage. By virtue of a large central hole the upper stage may be moved around the optical axis without the tedious turning of milled heads required by mechanical stages, or the fine touch (which takes some time for the student to acquire) needed in manipulating slides directly. Having used such a stage one quickly becomes adept at orienting the desired portion of any specimen. Because the stage is moved, rather than the slide one has the added advantage of not worrying about an errant stage clip knocking a cover slip from a temporary mount while chasing an active organism about the field of view.


Simplicity itself

As one can see in this illustration taken from a maintenance pamphlet published by American Optical, the stage is almost supernaturally simple. No doubt the company used the simplicity of the Micro-Glide Stage to its advantage. Such an apparatus is far less complex than the circular mechanical stages seen on research microscopes, and would have provided American Optical a bit of an edge in marketing their microscopes to schools (an important client for nearly all manufacturers).

The utility of a rotate-able stage is not something one often has to convince a microscopist of, and no attempt will be made here to do so. Only, it has always been practice for schools (from grammar to graduate) to utilize a rugged and uncomplicated sort of microscope; it has however, been a rare thing for them to offer students the chance to use a rotate-able stage. For that reason alone many who use microscopes, even for professional reasons, have never made use of microscope bearing a rotate-able stage and will not feel the acute discomfort of lacking one.

While the great biological and petrographic stands with their finely machined circular stages are beyond the reach of most enthusiasts, or at least past the financial tolerance of spouses and parents, one can usually find an American Optical stand featuring a Micro-Glide stage for sale surplus or second-hand in the range of fifty dollars. At the risk of sounding the salesmen, I’d recommend searching one out. Below see a simple students model One-Sixty I prefer for looking at algae, living diatoms, rotifera, and all the bustle and huff in a drop of water.




Divisible Objectives and my Favorite Stand

Things have come and gone in microscopy through the years. Some have been happily put aside as inconvenient when new advances were made and others have been quietly forgotten. I for one lament the passing of divisible objectives. -K

For a great many years it was considered abnormal and a genuine extravagance for a microscopist, even a professional, to be in possession of more than one stand. Optical apparatus was expensive, prohibitively so. Before continuing permit me to digress and provide an bit of example; consider that in the 1930 bound catalog of Bausch & Lomb an achromatic objective of 2x magnification was priced at $5.00, the equivalent of $71.10 dollars today. One could also have a 10x for $8.00 ($113.76). The full complement of dry achromatic objectives with magnification spanning 2x to 60x, some eight objectives in all, would have cost the princely sum of $86.00, $1222.93 in todays dollars according to the consumer price index, and been beyond the means of even the well-funded.

It’s easy to understand that for most microscopists it proved sensible economically to purchase a middle of the range 10x objective and use it with a comparatively inexpensive low power ocular when less magnification was required switching to a more powerful ocular as nessacary. In part because of the expense some things were done that would not be considered sound by the standards of today. One of those things, which no doubt seems somewhat blasphemous to todays workers, is the divisible objective. They turn up not infrequently on stands dating to what I think of as the “Black & Brass” era with rarer examples in the “Fully Brass” period preceding and becoming most common in the “Fully Black” period after the first world war. I can only hope for forgiveness regarding my rude designations of time but this is all very general.

A divisible objective is one in which the front and back optical components may be separated to obtain lower magnification. Bausch & Lomb produced these prolifically in the 16mm size so that with the front component in place 10x magnification was provided, while the rear portion only provided approximately 4x. By purchasing a divisible objective one was effectively provided a 16mm and 32mm objective in one unit. Most of the manufacturers provided divisible objectives of one sort or an other but the divisible 10x was certainly the most common from any source.

In 1925 Bausch & Lomb was granted a patent for a new system of constructing parfocal objectives that no doubt grew out of observations made while manipulating divisible objectives. The patent may however, have been an effort to cut down on competitors production of divisible objectives more than anything else, as the usual method of employing rings of varying thickness around the threads seems a great deal more convenient.


For comparison

Above one may see a B&L 32mm objective, 40mm objective, and 32mm equivalent portion of a divisible 16mm objective. It’s worth noting the differing position of the optical components of the objectives and that any of these objectives will work usefully on a compound microscope. The stand seen below is a perfect example of the sort of microscope on which one could expect to find a divisible objective.


No clips because I never incline my microscopes, it being my habit to work standing

The above is a Bausch & Lomb stand from the late 1940’s (easily dated by the double knurled heads). One can see the assembled 10x divisible objective in position and compare its outline with that of a non-divisible objective. This is in fact my favorite stand for micrography, photomicrography, measuring, and most general work, it shows every evidence of having been an economically prudent apparatus while not neglecting function.

This particular stand was assembled by Lukas Microscope Service of Skokie, Illinois. The company was founded in 1931 and is still in business today. They provided this microscope with a fixed, removable, 1.20 Numerical Aperture Abbe condenser with iris diaphragm and filter holder, the usual two sided mirror, and three objective turret. I keep a divisible 10x B&L, a 43x B&L, and a high dry 60x B&L in place on this stand and find few objectives more suitable for measuring the thickness of a mounted specimen than the 60x.

One final point concerning this lovely instrument, it is the most modern model I own which retains a draw tube. For any who are products of the modern age and have not had the pleasure I will say a draw tube can be unspeakably useful. Properly dispositioned it’s the work of a moment to compensate for an unexpectedly thick (or thin) cover glass, or increase or decrease magnification. Of course there are attendant sacrifices optically but I can’t count the times I’ve been able to better measure the size of a structure because I’m familiar with the workings of a draw tube for given combinations of objective and ocular.