Using the Microscope.
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Page 3. Magnification and Image Detail.
Of the two main design criteria which specify the performance of a microscope objective, N.A. is perhaps the most important in that it defines the limit of detail which can be resolved by the lens. The other important criterion is magnification, which determines at what degree of enlargement that detail is presented to the eye.
When an operator views an image through a correctly adjusted microscope, the eye lens is totally relaxed as though viewing a distant horizon -- the eye is focused for infinity. The focus mechanisms of the microscope bring to the relaxed eyes of its operator a sharp image of any object in the field of view. But any image arriving at the eye from infinity must be infinitely magnified. This would imply that all optical devices producing an aerial image have the same infinite magnification in spite of our experience that some images are definitely more magnified than others.
This anomaly was resolved some time in the nineteenth century by deciding that 10 inches (250 mm) was a suitable close viewing distance for most people to see the finest detail of which the eye is capable, and that magnifications could then be calculated if it was assumed that the image seen in the eyepiece of a microscope was actually located in space at a plane ten inches from the eyes of the operator. At that distance (or any distance short of infinity) all features of the image would have calculable dimensions, and would therefore be comparable to other images measured in the same plane.
The actual magnification is determined by using a object of known size, and then measuring the size of its image when projected 250mm from the exit pupil of the instrument -- in the case of the microscope, 250mm from the Ramsden disc of the eyepiece. Conversely, the size of any feature of the object can be determined by measuring the size of that feature's image, and dividing by the magnification.
This standard is still in use today in that the magnifying power of simple lenses and lens systems is determined by dividing their focal length into 250 mm. For example, a hand magnifier with a focal length of 25 mm is a ten-power magnifier.
For many years in the 1800s, English microscope manufacturers produced, in observance of this standard, microscopes having a tubelength (between objective and eyepiece) of ten inches, but these proved unwieldy in use. Until the quite recent development of infinity-corrected objectives and for most of the twentieth century, the accepted standard for microscope objectives was an optical tubelength of 160 mm. In other words, a microscope objective produced an image of the stated magnification only when it projected its image a distance of 160 mm measured from its back focal plane. This was also the conjugate distance required for spherical correction of the magnified image -- a topic dealt with in more detail in the advanced tutorial.
According to these criteria, a microscope objective having a focal length of 16mm is a ten-power objective (160 divided by 16), a forty-power objective has a focal length of 4mm, and so on.
An objective would of course produce larger or smaller magnifications with greater or lesser projection distances, but only at an optical tubelength of 160 mm was it both corrected for spherical aberration and delivering the engraved magnification.
Such is the magnification of the image which arrives at the plane of the eyepiece diaphragm in a properly set up microscope. What magnification should this eyepiece have?
The general answer would be -- enough extra magnification for an operator of good/normal vision to see all the detail in the image. So with regard to magnification, there is a close relationship between NA (as a measure of the amount of detail in the image), and the visual acuity of the person using the microscope.
Based upon long experience, it has been said that the microscope should have a total magnification of around a thousand times the NA of the objective for a person of good vision to see all the detail the image has to offer. People of better than average vision could see the detail at lower magnification; people with less acute vision would require more.
According to this rule of thumb, a good quality x40 objective of 0.65 NA could use a x15 eyepiece and still look sharp (at x600), and a x100 oil-immersion objective of 1.30 NA would not be revealing all of its detail with x10 eyepieces (at x1000).
Given that the highest practically achievable NA is about 1.40 it follows that x1400 is the highest useful magnification obtainable before passing into what is generally called "empty magnification" -- giving enlargement of the image but revealing no more detail.
For the person of average eyesight using an expertly set up microscope of the highest correction, specimens of high contrast would probably still look good at x2000 -- which could be seen as the outer limit of useful magnification in the light microscope.
These observations apply to the visual use of the microscope. Different criteria apply to the recording of microscope images on film of various formats, and in video and other CCD cameras. These issues are dealt with in the advanced tutorials.