*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.