NUMERICAL APERTURE AND RESOLUTION

In an optical microscope, the numerical aperture of the objective is an important specification in determining the resolution, or the amount of detail the microscope can render. This is defined as shown in Fig. 1.

Fig. 1. Determination of the numerical aperture for a microscope objective. See text for details.

Let L be a line passing through a point P in the specimen to be examined, as well as through the center of the objective. Let K be a line passing through P and intersecting the outer edge of the objective lens opening. (It is assumed that this outer edge is circular.) Let q be the measure of the angle between lines L and K. Let M be the medium between the objective and the sample under examination. This medium M is usually air, but not always. Let r_m be the refractive index of M. Then the numerical aperture of the objective A_o is given by
A_o = r_m sin q
In general, the greater the value of Ao, the better is the resolution. There are three ways to increase the Ao of a microscope objective of a given focal length:
• The diameter of the objective can be increased.
• The value of r_m can be increased.
• The wavelength of the illuminating light can be decreased.
Large-diameter objectives having short focal lengths, thereby providing high magnification, are difficult to construct. Thus, when scientists want to examine an object in high detail, they can use blue light, which has a relatively short wavelength. Alternatively, or in addition, the medium M between the objective and the specimen can be changed to something with a high index of refraction, such as clear oil. This shortens the wavelength of the illuminating beam that strikes the objective because it slows down the speed of light in M. (Remember the relation between the speed of an electromagnetic disturbance, the wavelength, and the frequency!) A side effect of this tactic is a reduction in the effective magnification of the objective lens, but this can be compensated for by using an objective with a smaller radius of surface curvature or by increasing the distance between the objective and the eyepiece.
The use of monochromatic light rather than white light offers another advantage. Chromatic aberration affects the light passing through a microscope in the same way that it affects the light passing through a telescope. If the light has only one wavelength, chromatic aberration does not occur. In addition, the use of various colors of monochromatic light (red, orange, yellow, green, or blue) can accentuate structural or anatomic features in a specimen that do not always show up well in white light.