## Useful Magnification Range

In order to observe fine specimen detail in the optical microscope, the minute features present must be of sufficient contrast and project an intermediate image at an angle that is somewhat larger than the angular resolving power of the human eye. At a selected numerical aperture, when the microscope provides a magnified image that has a magnitude equal to the resolution limit of the human eye, additional magnification beyond this point does not result in the resolution of even smaller specimen detail.

The **range of useful magnification** for an objective/eyepiece combination is defined by the numerical aperture of the microscope optical system. There is a minimum magnification necessary for the detail present in an image to be resolved, and this value is usually rather arbitrarily set as 500 times the numerical aperture (500 x NA) and defined by the equation**:**

At the other end of the spectrum, the maximum useful magnification of an image is usually set at 1000 times the numerical aperture (1000 x NA) as given by the equation above. Magnifications higher than this value will yield no further useful information or finer resolution of image detail, and will usually lead to image degradation. **Table 1** catalogs the common objective/eyepiece combinations that lie in the range of useful magnification.

**Table 1**- Range of Useful Magnification (500-100 x NA of Objective)

Objective | Eyepieces | ||||
---|---|---|---|---|---|

(NA) | 10x | 12.5x | 15x | 20x | 25x |

2.5x (0.08) | — | — | — | x | x |

4x (0.12) | — | — | x | x | x |

10x (0.35) | — | x | x | x | x |

20x (0.55) | x | x | x | x | x |

40x (0.70) | x | x | x | x | — |

60x (0.95) | x | x | x | — | — |

100x (1.42) | x | x | — | — | — |

Exceeding the limit of useful magnification causes the image to suffer from the phenomenon of **empty magnification** (illustrated in **Figure 1(b)**), where increasing magnification through the eyepiece or intermediate tube lens only causes the image to become more magnified with no corresponding increase in detail resolution. In contrast, the image shown in **Figure 1(a)** was captured using the correct objective and eyepiece combination to effectively utilize the numerical aperture to achieve optimum resolution.

In fact, excessive magnification introduces artifacts, diffraction boundaries, and halos into the image that obscure specimen features and complicate the interpretation of visual observations. Microscope observations are also affected by the sensitivity of the human eye to the intensity and color temperature of the illumination, the age of the observer, the presence of **floaters** in the eye, and whether the eye is rested or fatigued.

For visual observation, the image of the specimen fine structure must be viewed at an angle slightly larger than the resolving power of the human eye. With a microscope having good illumination, the distance between two resolved points in the specimen viewed at the reference visual distance of 250 millimeters is about 0.15 millimeters, corresponding to a **visual acuity** angle of about 2 minutes of arc. This limiting angle is restricted by the separation distance of visual elements in the retina, which are spaced about five microns apart.

To relate the limit of resolution of the eye and the resolving power of the objective, two closely spaced points in the specimen can be considered. If the two points reside at the limit of the objective's resolving power, then**:**

where **r** is the distance separating the two points, **λ** is the wavelength of illumination, and **NA**is the objective numerical aperture. In order to magnify the distance until the specimen points appear to the eye at a separation distance of 0.15 millimeters (representing 2 minutes of arc), we examine the relationship**:**

which can be rearranged to:

where **M** is the optimum microscope magnification. When the illuminating wavelength is assumed to lie in the green region of the visible light spectrum (550 nanometers or 0.00055 millimeters), we can substitute into the equation**:**

The result is the minimum magnification for visual observation of the finely spaced specimen detail, which is about 500 times the objective numerical aperture. This discussion applies to specimens having medium contrast, but with specimens of higher contrast the two points can be resolved by higher magnifications even if they are closer to each other. In practice, magnifications deviating considerably from the useful magnification range are often employed. For example, very low magnifications (1x through 4x) are often used to topographically map a specimen (such as a histologically stained thin section) where a wide field of view is desirable in order to quickly note all available specimen features. In many cases, a 2.5x objective may be combined with a wide field eyepiece at 10x magnification to reveal an area having a diameter of 8 millimeters or greater.

At high magnifications, the limit of useful magnification is sometimes exceeded in order to view the image more comfortably. This is often the case when small particles or organisms are observed and counted at very high numerical apertures and magnifications. Sharpness in the specimen details is then sacrificed, which usually does not interfere with quantitative analysis of the image.

Care should be taken in choosing eyepiece/objective combinations to ensure the optimal magnification of specimen detail without adding unnecessary artifacts. For instance, to achieve a magnification of 250x, the microscopist could choose a 25x eyepiece coupled to a 10x objective. An alternative choice for the same magnification would be a 10x eyepiece with a 25x objective. Because the 25x objective has a higher numerical aperture (approximately 0.65) than does the 10x objective (approximately 0.25), and considering that numerical aperture values define an objective's resolution, it is clear that the latter choice would be the best. If photomicrographs of the same viewfield were made with each objective/eyepiece combination described above, it would be obvious that the 10x eyepiece/25x objective duo would produce photomicrographs that excelled in specimen detail and clarity when compared to the alternative combination.

### Contributing Authors

**Kenneth R. Spring** - Scientific Consultant, Lusby, Maryland, 20657.

**Michael W. Davidson** - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.