Astronomical Telescope: Refracting Type

A refracting astronomical telescope, like the compound microscope, uses two convex lenses, but is built to view an object that is enormous in actual size yet so far away that it already subtends only a very small angle at the unaided eye (a planet, the moon, a distant star cluster) -- the opposite practical problem from a microscope's tiny, nearby object. The objective lens, of comparatively large diameter (to gather as much of the very faint incoming light as possible) and long focal length $f_o$, forms a real, inverted, and typically much smaller image of the distant object at (very nearly) its own focus, since the object is effectively at infinity. This real image is then viewed through the eyepiece, of comparatively short focal length $f_e$, positioned and used as a simple magnifier so that it takes this small real image and magnifies it further into an enlarged final image. In the telescope's normal adjustment, the eyepiece is positioned so that the objective's real image falls exactly at the eyepiece's own focus as well, so that the final image is thrown out to infinity and can be viewed by a fully relaxed (unaccommodated) eye; under this normal adjustment the magnifying power works out simply as the ratio of the two focal lengths, $M=\frac{f_o}{f_e},$ and, since both the objective's real image and the eyepiece's own focus coincide at the very same point between the two lenses under this adjustment, the overall length of the telescope tube is simply the sum of the two focal lengths, $L=f_o+f_e$. This formula makes the telescope designer's central trade-off explicit: high magnifying power calls for a …