Introduction
Optical microscopes are designed to greatly magnify the images of objects too small to resolve with the unaided eye. Microscopes, in contrast to telescopes, work at close range. The design is in some ways similar to that of the telescope, but in other ways it differs. The simplest microscopes consist of single convex lenses. These can provide magnification factors of up to 10× or 20×. In the laboratory, an instrument called the compound microscope is preferred because it allows for much greater magnification.
Basic Principle
A compound microscope employs two lenses. The objective has a short focal length, in some cases 1 mm or less, and is placed near the specimen or sample to be observed. This produces an image at some distance above the objective, where the light rays come to a focus. The distance (let’s call it s) between the objective and this image is always greater than the focal length of the objective.
The eyepiece has a longer focal length than the objective. It magnifies the real image produced by the objective. In a typical microscope, illumination can be provided by shining a light upward through the sample if the sample is translucent. Some microscopes allow for light to be shone downward on opaque specimens. Figure 19-13 is a simplified diagram of a compound microscope showing how the light rays are focused and how the specimen can be illuminated.
Fig. 19-13. Illumination and focusing in a compound optical microscope.
Laboratory-grade compound microscopes have two or more objectives, which can be selected by rotating a wheel to which each objective is attached. This provides several different levels of magnification for a given eyepiece. In general, as the focal length of the objective becomes shorter, the magnification of the microscope increases. Some compound microscopes can magnify images up to about 2,500 times. A hobby-grade compound microscope can provide decent image quality at magnifications of up to about 1,000 times.
Focusing
A compound microscope is focused by moving the entire assembly, including both the eyepiece and the objective, up and down. This must be done with a precision mechanism because the depth of field (the difference between the shortest and the greatest distance from the objective at which an object is in good focus) is exceedingly small. In general, the shorter the focal length of the objective, the smaller is the depth of field, and the more critical is the focusing. High-magnification objectives have depths of field on the order of 2 μm (2 × 10 ^{−6}m) or even less.
If the eyepiece is moved up and down in the microscope tube assembly while the objective remains in a fixed position, the magnification varies. However, microscopes usually are designed to provide the best image quality for a specific eyepiece-to-objective separation, such as 16 cm (approximately 6.3 in).
If a bright enough lamp is used to illuminate the specimen under examination, and especially if the specimen is transparent or translucent so that it can be lit from behind, the eyepiece can be removed from the microscope and a decent image can be projected onto a screen on the ceiling of the room. A diagonal mirror can reflect this image to a screen mounted on a wall. This technique works best for objectives having long focal lengths, and hence low magnification factors.
Microscope Magnification
Refer to Fig. 19-14. Suppose that f _{o} is the focal length (in meters) of the objective lens and f _{e} is the focal length (in meters) of the eyepiece. Assume that the objective and the eyepiece are placed along a common axis and that the distance between their centers is adjusted for proper focus. Let s represent the distance (in meters) from the objective to the real image it forms of the object under examination. The microscopic magnification (a dimensionless quantity denoted m in this context) is given by
m = [( s − f _{o} )/ f _{o} )] [( f _{e} + 0.25)/ f _{e} ]
Fig. 19-14 . Calculation of the magnification factor in a compound microscope. See text for details.
The quantity 0.25 represents the average near point of the human eye, which is the closest distance over which the eye can focus on an object: approximately 0.25 m.
A less formal method of calculating the magnification of a microscope is to multiply the magnification of the objective by the magnification of the eyepiece. These numbers are provided with objectives and eyepieces and are based on the use of an air medium between the objective and the specimen, as well as on the standard distance between the objective and the eyepiece. If m _{e} is the power of the eyepiece and m _{o} is the power of the objective, then the power m of the microscope as a whole is
m = m _{e} m _{o}
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. 19-15.
Fig. 19-15 . 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 A _{o} , the better is the resolution. There are three ways to increase the A _{o} 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.
The Compound Microscope Practice Problem
Problem
A compound microscope objective is specified as 10×, whereas the eyepiece is rated at 5×. What is the power m of this instrument?
Solution
Multiply the magnification factor of the objective by that of the eyepiece:
m = (5 × 10) × = 50×
Practice problems of these concepts can be found at: Optics Practice Test
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From Physics Demystified: A Self-Teaching Guide. Copyright © 2002 by The McGraw-Hill Companies, Inc. All Rights Reserved.