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Ray 1 I1 di Principal plane O1 do Principal plane
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Section 172 Curved Mirrors
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Figure 17-1 A Gregorian 1 telescope produces a real image that is upright
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Secondary concave mirror
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How can the inverted real image created by a concave mirror be turned right-side up In 1663, Scottish astronomer James Gregory developed the Gregorian telescope, shown in Figure 17-11, to resolve this problem It is composed of a large concave mirror and a small concave mirror arranged such that the smaller mirror is outside of the focal point of the larger mirror Parallel rays of light from distant objects strike the larger mirror and reflect toward the smaller mirror The rays then reflect off the smaller mirror and form a real image that is oriented exactly as the object is
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Use the following strategies for spherical-mirror problems Refer to Figure 17-10 1 Using lined or graph paper, draw the principal axis of the mirror as a horizontal line from the left side to the right side of your paper, leaving six blank lines above and six blank lines below 2 Place a point and a label on the principal axis the object, C, and F, as follows a If the mirror is a concave mirror and the object is beyond C, away from the mirror, place the mirror at the right side of the page, place the object at the left side of the page, and place C and F to scale b If the mirror is a concave mirror and the object is between C and F, place the mirror at the right side of the page, place C at the center of the paper, F halfway between the mirror and C, and the object to scale c For any other situation, place the mirror in the center of the page Place the object or F (whichever is the greatest distance from the mirror) at the left side of the page, and place the other to scale 3 To represent the mirror, draw a vertical line at the mirror point that extends the full 12 lines of space This is the principal plane 4 Draw the object as an arrow and label its top O1 For concave mirrors, objects inside of C should not be higher than three lines high For all other situations, the objects should be six lines high The scale for the height of the object will be different from the scale along the principal axis 5 Draw ray 1, the parallel ray It is parallel to the principal axis and reflects off the principal plane and passes through F 6 Draw ray 2, the focus ray It passes through F, reflects off the principal plane, and is reflected parallel to the principal axis 7 The image is located where rays 1 and 2 (or their sight lines) cross after reflection Label the point I1 The image is an arrow perpendicular from the principal axis to I1
17 Reflection and Mirrors
Lick Observatory
Mirror diameter
Figure 17-12 A concave spherical mirror reflects some rays, such that they converge at points other than the focus (a) A parabolic mirror focuses all parallel rays at a point (b)
Real image defects in concave mirrors In tracing rays, you have reflected the rays from the principal plane, which is a vertical line representing the mirror In reality, rays are reflected off the mirror itself, as shown in Figure 17-12a Notice that only parallel rays that are close to the principal axis, or paraxial rays, are reflected through the focal point Other rays converge at points closer to the mirror The image formed by parallel rays reflecting off a spherical mirror with a large mirror diameter and a small radius of curvature is a disk, not a point This effect, called spherical aberration, makes an image look fuzzy, not sharp A mirror ground to the shape of a parabola, as in Figure 17-12b, suffers no spherical aberration Because of the cost of manufacturing large, perfectly parabolic mirrors, many of the newest telescopes use spherical mirrors and smaller, specially-designed secondary mirrors or lenses to correct for spherical aberration Also, spherical aberration is reduced as the ratio of the mirror s diameter, shown in Figure 17-12a, to its radius of curvature is reduced Thus, lower-cost spherical mirrors can be used in lower-precision applications
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