# Numerical Aperture and Magnification Effects

In optical microscopy, image brightness is governed by the light-gathering power of the objective, which is a function of numerical aperture. Magnification also plays a role in determining the brightness as explored in this interactive tutorial.

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The tutorial initializes with the objective magnification set to 10x and a numerical aperture value of 0.15, which is adjustable using the Numerical Aperture slider. As the slider is translated to higher numerical apertures at a fixed magnification, the light cone size changes and the image brightness (intensity) values for transmitted and reflected light illumination modes are computed and displayed in red letters. To select another magnification, use the Magnification pull-down menu to choose an objective in the range between 10x and 100x. Note that at lower numerical apertures and magnifications, the transmitted illumination intensity is greater than that observed with the same objective in reflected light. These values reverse themselves at higher numerical apertures and magnifications with the reflected light intensities becoming much greater than those observed in transmitted light.

Image brightness is directly proportional to the objective numerical aperture and inversely proportional to the square of the lateral magnification:

Image Brightness µ (NA/M)2

where NA is the objective numerical aperture and M is the magnification. The ratio given in the equation above expresses the light-gathering power of the objective in transillumination (note: the case with epi-illumination is somewhat different, as discussed below). In general, objectives with high numerical apertures are also better corrected for aberrations. Thus, for the same magnification, higher numerical aperture objectives collect more light, produce a brighter and better-corrected image, and the overall image is better resolved.

When an objective is used in transillumination, image brightness decreases rapidly as the magnification increases. In contrast, utilization of a specific objective for epi-illumination produces increasingly brighter images as the magnification increases. The terms F(trans) and F(epi) refer to the light-gathering power of an objective and were calculated according to the following equations:

F(trans) = 104 • NA2/M2

F(epi) = 104 • (NA2/M)2

In theory, the intensity of illumination depends on the square of the condenser numerical aperture and the square of the demagnification of the light source image (in effect, the field diaphragm image becomes brighter as it is made smaller, according to the square law). The result is that brightness of the specimen image is directly proportional to the square of the objective numerical aperture as it reaches the eyepiece (or camera system), and also inversely proportional to the objective magnification. Therefore, when examining specimens in transmitted light, changing the objective without altering the condenser affects image brightness in response to changes in numerical aperture and magnification.

#### Contributing Authors

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

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