The Bausch & Lomb Model R part: III

The question of the determination of a microscopes magnification has a distinct tendency to be treated in either a profoundly technical way or only the most basic terms, never mind the source. On the simpler end of things it’s often put similarly to this: the magnifying power of a microscope is determined by multiplying the power of the objective by that of the ocular. Well, lovely. That certainly buttons that up doesn’t it, no? There may even be a few lines here of there on the power of an objective or ocular but all such texts take it as given that the optical components will be marked. At the opposite end of the spectrum one will find page after page of complex optical formulae and jargon like principle poster focus and Ramsden disc. Fortunately those formulae that are printed can be made rather more meaningful to most people by simply substituting words for symbols, as such:

Magnifying Power = Tube Length x Distance of Distinct Vision / Focal Length of Objective x Focal Length of Eyepiece

Which is great, if you want to muck about in physics class and measure the focal length of your lenses. One could of course forego that in favor of a little bit of basic math, if one had an eyepiece micrometer and an object micrometer, but then the Model R uses non-standard diameter optics so the chances one has an reticule of the right size for the narrow ocular is slim, and in any case it’s a closed system-not something one would easily disassemble. So what if you haven’t got anything, not even a stage micrometer? I mean the Model R was made for kids right, what kid just happened to have a hankering for a stage micrometer first thing when they got a microscope? Alright, maybe a lot of us did, so we’ll use one but bear in mind we can do this with any object that has a known diameter, like a human red blood cell (7.2 microns at the widest point) or a human hair (in the neighborhood of 70 microns is diameter.

All the physics used to determine magnification is well and good but pales as a practical exercise for the microscopist to comparing the known size of a particular object to the magnified size of that object. In order to do that with math one needs to know a great many things about the lenses to begin with, most of which is best suited for classwork in physics only. In order to make the same comparison in an almost exclusively practical way one need only set up the Model R (or any microscope) as below.

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  1. Place the object of known size (be it a blood smear or stage micrometer) on the stage and focus the microscope.
  2. Incline the joint so that the microscope is horizontal The Model R hasn’t got an inclination joint but the body and stage comes off from the foot and may be mounted horizontally.
  3. Use a rule to position the exit pupil of the microscope 250mm from a sheet of paper taped to a wall or other support.
  4. Position a bright, high intensity light source so that it may be focused on the specimen from below the substage.
  5. Turn out the room lights.
  6. Mark the locations of several divisions of the micrometer or a few red blood cells on the paper.

Now that the paper has been marked only one further measurement is required. The marks made by projecting the specimen on the paper are of a known division. They are also of a size that may be easily measured with convention means.

  1. Use a rule marked in millimeters to measure the divisions marked on the paper.
  2. Line up carefully and note the number of divisions on the paper that are needed to span the distance perfectly between any given number of either.
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Yes, I did chose to awkwardly lean over the entire setup rather than walk to the other side of the table!

Now for the math, in this case the formula is much simpler than one might expect. One need only divide the distance as measured on the ruler by the known measurement of the magnified and enlarged divisions marked on the paper. Therefore if the divisions of the stage micrometer are 0.01mm, and at the Model R’s most powerful magnification (draw tube fully extended) they measure precisely 4 divisions in 12mm the formulae would be 12/0.04 = 300 diameters of magnification. It’s pretty nice to see that that confirms the marking on the draw tube. Repeating the process with the draw tube fully retracted one finds that 2 divisions as marked on the paper span 3mm exactly, 3/0.02=150 diameters of magnification.

With this knowledge one can accept that the marked powers on the draw tube are accurate, but that doesn’t inform on the individual power of either the objective or ocular. One will of course recognize that removing the front element serves to reduce the power of the entire system by half as that is what the markings indicate. Unfortunately this does not enable one to know the power of the individual elements. One need only repeat the process without the ocular to find the power of the objective alone. It then becomes a simple matter to know the power of the ocular, power of the entire system / power of the objective = power of the ocular.

Repeating the steps above, except to this time measure 250mm from the rear of the objective lens provides the following measurement. Twenty divisions (marked in intervals of 5 each) measures 4mm on the paper. Such that, 4/0.2=20 meaning the power of the objective is 20x and the ocular is therefore 15x which further indicates that removing the front lens element reduces the power of the objective to 10x.

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Determining Objective Magnification

Here’s hoping this is useful as more than just an academic exercise. -K

In the previous post we looked at equivalent focus as it relates to the power of an objective. It was noted that the power marked explicitly on ones objective is sometimes at odds with that implied by the equivalent focus. Today we’ll look at one way to determine the actual power of a given objective. The method used is among the more equipment heavy, but it is also one of the least demanding so far as manipulations go.

One will need the following:

  • A microscope with a draw tube (or an eyepiece collar)
  • A 10x Huygenian eyepiece
  • A 10x Ramsden eyepiece
  • A stage micrometer
  • An ocular micrometer (installed in the Ramsden eyepiece)

Method

Using the Huygenian ocular, with the stage micrometer as an object, and the draw tube set to the length for which the objective is corrected (160 in most cases) the objective to be measured is brought into sharp focus. The Huygenian ocular is then replaced with the Ramsden and everything brought into sharp focus by moving in or out the draw tube. One must not focus using the microscopes coarse or fine adjustments.

Line up the rulings of the stage micrometer so that a given number corresponds with a particular span of the rulings on the ocular micrometer. Be sure that the rulings are lined up consistently, do not measure from the outside of the line in one place and the inside in another. Use as much of the available rulings as possible for increased accuracy. Write down the rulings on the stage micrometer that are required and the corresponding number from the ocular.

Now divide the distance of the rulings on the ocular by the distance of the rulings on the stage. The dividend is the ocular independent magnification of the objective.

In Practice

A stage micrometer is measured against the Ramsden micrometer eyepiece as described above. Rulings on the stage micrometer are .01mm apart and rulings on the eyepiece micrometer are .1mm apart. It is found that 95 rulings on the stage micrometer correspond exactly to 98 rulings on the eyepiece micrometer.

9.8mm / .95mm = 10.3

The objective then, provides 10.3X magnification.

With a different objective it is found that 15 rulings on the stage micrometer correspond to 65 rulings on the eyepiece micrometer. Once again we work in consistent units of measure.

9.3mm / .22mm = 42.27

The objective then, provides 42.27X magnification.

In Theory

Some users may immediately wonder why it is emphasized that one must focus with a Huygenian ocular, only to replace it with a Ramsden fitted with a micrometer, and manipulate the draw tube for focus. Why shouldn’t one simply use a Huygenian ocular fitted with a micrometer? After all it works for measuring structures.

First consider the construction of a Ramsden ocular. The positive ocular forms a real image below its field lens, outside of the influence of the oculars magnification. A Hugenian ocular, a negative ocular, only forms a real image after light from the objective passes through its field lens. The upshot of which is that a Huygenian ocular will measure an objective as more powerful than it is.

Why then does it mater if one focuses with a negative ocular like the Huygenian but measures with a positive ocular like the Ramsden? The simple explanation is that doing so negates the magnification that results from the eye viewing a virtual image on which a real image of a ruled reticule has been overlaid. Using the Ramsden only will again result in a distortion of the objectives power.

Notes:

∗An eyepiece collar is a small, friction fit, split disc which rides around the outside barrel of an eyepiece and prevents it from seating fully into the microscopes body tube. Such a collar can provide a microscope not equipped with a draw tube with much of the same functionality.

†A Huygenian filar micrometer used with the objectives above measures their powers as 11.37X and 47.8X respectively.

‡In this case the Ramsden eyepiece alone measures the objectives powers as 10.2X and 43.3X. These distortions represent the degree to which the focus was adjusted by manipulation of the draw tube after switching from the Hugenian ocular to the Ramsden.