26.12

The Compound Microscope

To increase the angular magnification beyond that possible with a magnifying glass, an additional converging lens can be included to “premagnify” the object before the magnifying glass comes into play. The result is an optical instrument known as the compound microscope (Figure 26-41). As discussed in Section 26.9, the magnifying glass is called the eyepiece, and the additional lens is called the objective.

Figure 26-41 A compound microscope.

The physics of the compound microscope.

The angular magnification of the compound microscope is (Equation 26.9), where is the angular size of the final image and is the reference angular size. As with the magnifying glass in Figure 26-40, the reference angular size is determined by the height ho of the object when the object is located at the near point of the unaided eye: , where N is the distance between the eye and the near point. Assuming that the object is placed just outside the focal point Fo of the objective (see Figure 26-33a) and that the final image is very far from the eyepiece (i.e., near infinity; see Figure 26-33c), it can be shown that

| (26.11)

In Equation 26.11, fo and fe are, respectively, the focal lengths of the objective and the eyepiece. The angular magnification is greatest when fo and fe are as small as possible (since they are in the denominator in Equation 26.11) and when the distance L between the lenses is as large as possible. Furthermore, L must be greater than the sum of fo and fe for this equation to be valid. Example 16 deals with the angular magnification of a compound microscope.

| Example 16 | | | The Angular Magnification of a Compound Microscope

The focal length of the objective of a compound microscope is fo = 0.40 cm, and that of the eyepiece is fe = 3.0 cm. The two lenses are separated by a distance of L = 20.0 cm. A person with a near point distance of N = 25 cm is using the microscope. (a) Determine the angular magnification of the microscope. (b) Compare the answer in part (a) with the largest angular magnification obtainable by using the eyepiece alone as a magnifying glass.
Reasoning The angular magnification of the compound microscope can be obtained directly from Equation 26.11, since all the variables are known. When the eyepiece is used alone as a magnifying glass, as in Figure 26-40b, the largest angular magnification occurs when the image seen through the eyepiece is as close as possible to the eye. The image in this case is at the near point, and according to Equation 26.10, the angular magnification is .
Solution

a. | The angular magnification of the compound microscope is

The minus sign indicates that the final image is inverted relative to the initial object.
b. | The maximum angular magnification of the eyepiece by itself is

The effect of the objective is to increase the angular magnification of the compound microscope by a factor of 350/9.3 = 38 compared to that of a magnifying glass.

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