Beware of "Empty" Magnification

May 18, 2008

In the simplest case, an optical microscope consists of one lens close to the specimen (objective) and one lens close to the eye (eyepiece). The microscope magnification is the product of the factors of both microscope lenses. A 40x objective and a 10x eyepiece, for example, provide a 400x magnification.

The light wave defines the limit

However, it is not only the magnification but also the resolution that indicates the performance capacity of an optical microscope. Resolution is the ability to render two closely adjacent dots separately. According to the Rayleigh criterion, the minimum distance between two dots able to be separately imaged corresponds to approximately one-half the wavelength of the light.

λ = light wavelength
n = refractive index of the medium between specimen and  objective
α = half the aperture angle of the objective

Therefore, with blue light, the resolution limit is approximately d = 0.2 μm; with red light, around d = 0.35 μm. UV objectives attain a resolution just under 0.2 μm. With the naked eye, we are not able to differentiate structures smaller than 0.2 millimetres.

The value n × sin α corresponds to the numerical aperture (NA), the measure of the light gathering capacity and the resolution of an objective. Because the aperture angle cannot exceed 90° and the refractive index is never less than 1 (nair = 1), NA is always around 1 for air. When immersion oil is used (n > 1), the numerical aperture increases (to up to approx. 1.45) and, along with it, the resolution.

Fig. 1: The spectrum of visible light
Resolution Limit
numerical aperture

Fig. 2: The numerical aperture of the objective determines the detail resolution and brightness of the image

More magnification is not always better

To make the microscopic resolution detectable to the eye, the image appears in the eyepiece with corresponding magnification. The resolution and magnification are always directly interdependent. An objective with low magnification has a low numerical aperture and thus a low resolution. For a high-magnification objective, the numerical aperture is also high, typically 0.8 for a 40x dry objective. However, because the numerical aperture cannot be increased beyond a certain point, the usable magnification range is also limited in classic light microscopes. The "useful" microscope magnification is between 500 × NA and 1,000 × NA.

Some light microscopes boast enormous magnification, but practically speaking, the limit is just under 1,400x. Specialists call everything beyond that "empty magnification." Though structures appear larger, but no additional details are resolved.

Fig. 3: Hard metal with 10 % cobalt (sub-µm structure, 0.6 µm initial grain size) for production of heavy-duty tools. Left: viewed with dry objective, NA = 0.90; right: viewed with oil immersion objective, NA = 1.30 (Courtesy of Konrad Friedrichs GmbH & Co KG, Kulmbach, Germany)

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