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Figure 17-7 At A a concave mirror focuses parallel light rays to a point
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At B the same mirror collimates light from a point source at the focus
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Optics and Telescopes
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area, the greater is the light-gathering power The smaller the radius of curvature, the shorter is the focal length If you look at your reflection in a convex mirror, you will see the same effect that you would observe if you placed a convex lens up against a flat mirror Concave mirrors can have spherical surfaces, but the finest mirrors have surfaces that follow the contour of an idealized three-dimensional figure called a paraboloid A paraboloid results from the rotation of a parabola, such as that having the equation y x2 in rectangular coordinates, around its axis When the radius of curvature is large compared with the size of the reflecting surface, the difference between a spherical mirror and a paraboloidal mirror (more commonly called a parabolic mirror) is not noticeable to the casual observer However, it makes a big difference when the mirror is used in a telescope
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The first telescopes were developed in the 1600s and used lenses Any telescope that enlarges distant images with lenses alone is called a refracting telescope
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GALILEAN REFRACTOR
Galileo devised a telescope consisting of a convex-lens objective and a concave-lens eyepiece His first telescope magnified the apparent diameters of distant objects by a factor of only a few times Some of his later telescopes magnified up to 30 times The Galilean refractor (Fig 17-8A) produces an erect image, that is, a right-side up view of things In addition to appearing right-side-up, images are also true in the left-to-right sense The magnification factor, defined as the number of times the angular diameters of distant objects are increased, depends on the focal length of the objective, as well as on the distance between the objective and the eyepiece Galilean refractors are still available today, mainly as novelties for terrestrial viewing Galileo s original refractors had objective lenses only 2 or 3 cm (about 1 in) across; the same is true of most Galilean telescopes found today Some of these telescopes have sliding, concentric tubes, providing variable magnification When the inner tube is pushed all the way into the
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PART 5
Space Observation and Travel
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Figure 17-8 The Galilean refractor (A) uses a convex objective and a concave eyepiece The Keplerian refractor (B) has a convex objective and a convex eyepiece
outer one, the magnification factor is the lowest; when the inner tube is pulled all the way out, the magnification is highest The image remains fairly clear over the entire magnification-adjustment range These instruments are sometimes called spy glasses
KEPLERIAN REFRACTOR
Johannes Kepler s refracting telescope employed a convex-lens objective with a long focal length and a smaller convex-lens eyepiece with a short focal length Unlike the Galilean telescope, the Keplerian refractor (see Fig 17-8B) produces an inverted image; it is upside-down and backwards The distance between the objective and the eyepiece must be exactly equal to the sum of the focal lengths of the two lenses in order for the image to be clear The magnification factor depends on the ratio between the focal lengths of the objective and the eyepiece
Optics and Telescopes
The Keplerian telescope is preferred over the Galilean type mainly because the Keplerian design provides a larger apparent field of view This is the angular diameter, as seen directly by the eyes, of the circular region in which objects appear through the telescope Galilean telescopes have apparent fields of view so narrow that looking through them is an uncomfortable experience The magnification factor of a Keplerian telescope can be changed by using eyepieces with longer or shorter focal lengths The shorter the focal length of the eyepiece, the greater is the magnification factor, informally known as power, assuming that the focal length of the objective lens remains constant The largest refracting telescope in the world is a Keplerian refractor, located at the Yerkes Observatory in Wisconsin Its objective lens has a diameter of 40 in, or slightly more than 1 m Keplerian refractors are used by thousands of amateur astronomers worldwide
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