Physics · Ch 6 — Optics
Astronomical Telescope
Astronomical Telescope
An astronomical telescope is used to magnify the apparent size of distant astronomical objects -- stars, planets, the Moon -- and forms an inverted final image. It uses an objective of long focal length and large aperture, and an eyepiece of comparatively short focal length. Light from a distant object entering the objective forms a real image at the objective's own second focal point; the eyepi …
What this figure shows. Parallel rays from a distant astronomical object enter the long-focal-length objective (focal length fo) and converge to a real, inverted image at the objective's own second focal point, right at the tube's midpoint; the eyepiece (focal length fe), positioned so this real image sits at (or just inside) its own first focal point, then acts as a simple magnifier, producing a large final image at infinity for the relaxed eye. The angular size alpha of the original distant object and the angular size beta of the final magnified image, both marked on the diagram, are what the telescope …
Worked out. A telescope has objective focal length fo = 125 cm and eyepiece focal length fe = 2 cm. The angular magnification is m = fo/fe = 125/2 = 62.5, and the approximate telescope length is L = fo + fe = 127 cm = 1.27 m. Two stars whose true angular separation is 1 arcminute (1') will appear, viewed through this telescope, separated by theta(i) = m times theta(0) = 62.5 times 1' = 62.5' = 62.5/60 degrees, i.e. about 1.04 degrees apart -- turning a separation too fine for the naked eye to distinguish clearly into one spread comfortably over a full degree of app …