26.13

The Telescope

A telescope is an instrument for magnifying distant objects, such as stars and planets. Like a microscope, a telescope consists of an objective and an eyepiece (also called the ocular). Since the object is usually far away, the light rays striking the telescope are nearly parallel, and the “first image” is formed just beyond the focal point Fo of the objective, as Figure 26-42a illustrates. The first image is real and inverted. Unlike that in the compound microscope, however, this image is smaller than the object. If, as in part b of the drawing, the telescope is constructed so the first image lies just inside the focal point Fe of the eyepiece, the eyepiece acts like a magnifying glass. It forms a final image that is greatly enlarged, virtual, and located near infinity. This final image can then be viewed with a fully relaxed eye.

Figure 26-42 (a) An astronomical telescope is used to view distant objects. (Note the “break” in the principal axis, between the object and the objective.) The objective produces a real, inverted first image. (b) The eyepiece magnifies the first image to produce the final image near infinity.

The physics of the telescope.

The angular magnification M of a telescope, like that of a magnifying glass or a microscope, is the angular size subtended by the final image of the telescope divided by the reference angular size of the object. For an astronomical object, such as a planet, it is convenient to use as a reference the angular size of the object seen in the sky with the unaided eye. Since the object is far away, the angular size seen by the unaided eye is nearly the same as the angle subtended at the objective of the telescope in Figure 26-42a. Moreover, is also the angle subtended by the first image, so , where hi is the height of the first image and fo is the focal length of the objective. A minus sign has been inserted into this equation because the first image is inverted relative to the object and the image height hi is a negative number. The insertion of the minus sign ensures that the term , and hence , is a positive quantity. To obtain an expression for , refer to Figure 26-42b and note that the first image is located very near the focal point Fe of the eyepiece, which has a focal length fe. Therefore, . The angular magnification of the telescope is approximately

| (26.12)

The angular magnification is determined by the ratio of the focal length of the objective to the focal length of the eyepiece. For large angular magnifications, the objective should have a long focal length and the eyepiece a short one. Some of the design features of a telescope are the topic of the next example.

| Example 17 | | | The Angular Magnification of an Astronomical Telescope

The telescope shown in Figure 26-43 has the following specifications: fo = 985 mm and fe = 5.00 mm. From these data, find (a) the angular magnification of the telescope and (b) the approximate length of the telescope.

Figure 26-43 An astronomical telescope. The viewfinder is a separate small telescope with low magnification and serves as an aid in locating the object. Once the object has been found, the viewer looks through the eyepiece to obtain the full magnification of the telescope. (Tony Freeman/PhotoEdit)

Reasoning The angular magnification of the telescope follows directly from Equation 26.12, since the focal lengths of the objective and eyepiece are known. We can find the length of the telescope by noting that it is approximately equal to the distance L between the objective and eyepiece. Figure 26-42 shows that the first image is located just beyond the focal point Fo of the objective and just inside the focal point Fe of the eyepiece. These two focal points are, therefore, very close together, so the distance L is approximately the sum of the two focal lengths: .
Solution

a. | The angular magnification is approximately

| (26.12)

b. | The approximate length of the telescope is

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