A microscope magnifies small, nearby objects to look large. A telescope magnifies distant objects, which might be quite large, so that we can see details that are blended together when seen by eye.

FIGURE 35.15 shows the optical layout of a simple telescope. A large-diameter objective lens (larger lenses collect more light and thus can see fainter objects) collects the parallel rays from a distant object $(s=\text{∞})$ and forms a real, inverted image at distance $s\prime =f_{\text{obj}}$. Unlike a microscope, which uses a short-focal-length objective, the focal length of a telescope objective is very nearly the length of the telescope tube. Then, just as in the microscope, the eyepiece functions as a simple magnifier. The viewer observes an inverted image, but that’s not a serious problem in astronomy. Telescopes used to look at objects on earth have a somewhat different design to obtain an upright image.

FIGURE 35.15 A refracting telescope.

Suppose the distant object, as seen by the objective lens, subtends angle ${\theta }_{\text{obj}}$. If the image seen through the eyepiece subtends a larger angle ${\theta }_{\text{eye}}$, then the angular magnification is $M={\theta }_{\text{eye}}/{\theta }_{\text{obj}}$. We can see from the undeviated ray passing through the center of the objective lens that (using the small-angle approximation)

where the minus sign indicates the inverted image. The image of height $h\prime$ acts as the object for the eyepiece, and we can see that the final image observed by the viewer subtends angle

Consequently, the angular magnification of a telescope is

The angular magnification is simply the ratio of the objective focal length to the eyepiece focal length.

Because the stars and galaxies are so distant, light-gathering power is more important to astronomers than magnification. Large light-gathering power requires a large-diameter objective lens, but large lenses are not practical; they begin to sag under their own weight. Thus refracting telescopes, with two lenses, are relatively small. Serious astronomy is done with a reflecting telescope, such as the one shown in FIGURE 35.16.

FIGURE 35.16 A reflecting telescope.

A large-diameter mirror (the primary mirror) focuses the rays to form a real image, but, for practical reasons, a secondary mirror reflects the rays sideways before they reach a focus. This moves the primary mirror’s image out to the edge of the telescope where it can be viewed by an eyepiece on the side. None of these changes affects the overall analysis of the telescope, and its angular magnification is given by Equation 35.12 if $f_{\text{obj}}$ is replaced by $f_{\text{pri}}$, the focal length of the primary mirror.