Galilean, or terrestrial, telescopes consist of a lower-power positive lens (the objective) and a higher-power minus lens (the ocular, or eyepiece) separated by the difference in their focal lengths. Keplerian, or astronomical, telescopes consist of a lower-power positive objective lens and a higher-power positive eyepiece separated by the sum of their focal lengths (Figure 1-35). (Technically, the separation of the lenses is f1 − f2 for both types of telescopes because f2 is negative for the Keplerian telescope.) We can easily construct both types by using trial lenses. The Galilean telescope produces an upright image; the Keplerian, an inverted image. However, by placing prisms inside the Keplerian telescope, we can achieve an upright image. Most binoculars are Keplerian telescopes with inverting prisms.
In both types of telescope, an object ray parallel to the optic axis is conjugate to an image ray parallel to the axis. Consequently, the system considered as a whole has no focal points, and hence it is termed an afocal system. Also, considered as a whole, telescopes have no principal planes and no nodal points.
Figure 1-35 Ray tracing for 2 types of telescopes. A, A Galilean telescope consists of the objective (a lower-power plus lens) and the eyepiece, or ocular (a higher-power minus lens), separated by the difference of their focal lengths. B, A Keplerian telescope consists of a low-power plus lens (objective) and a higher-power plus lens (eyepiece). In both cases, an object ray parallel to the axis is conjugate to an image ray parallel to the axis. Consequently, although the individual lenses have focal points, the system as a whole does not.
(Courtesy of Edmond H. Thall, MD.)
Both types of telescope produce images smaller than the original object: MT = −P1/P2. In the examples shown in Figure 1-36, the image is half the size of the object (note the distance between the horizontal entering ray and the horizontal exiting ray). However, the image appears larger because it is much closer to the eye. In those examples, the image appears 4 times closer than the original object. Because the image is half the size of the original object but 4 times closer, the angle the image subtends and the appearance of the image are twice as large as the original object.
In general, we use telescopes to view objects at very great (“astronomical”) distances, for which transverse magnification is of little interest. It is more useful to describe the magnification in such a system in terms of the ratio of the angular separation between source objects as seen without the telescope and the angular separation between their images as seen through the telescope. We can show with careful ray tracing that this ratio, the angular magnification, is given by
Telescopes are often prescribed as visual aids for visually impaired patients (see Chapter 9). The Galilean telescope is generally preferred for visual aids because it is shorter than the Keplerian and produces an upright image. The Keplerian telescope can produce an upright image only by incorporating inverting prisms, which increase the weight of the visual aid. However, Keplerian telescopes gather more light than Galilean telescopes do—a quality that is advantageous in some situations.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.