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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.



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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)





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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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G Compilation fails due to errors on lines 11 and 12 Answer (for Objective 64): D is correct When a method takes a wildcard generic type, the collection can be accessed or modified, but not both The rest of the code is legal It s legal to add a subclass element to a typed collection It s legal for a method s argument to be a typed wildcarded interface A, B, C, E, F, and G are incorrect based on the above

Figure 8-3 shows the popular G5RV antenna Although not without some problems, this antenna is very popular It can be used either as a horizontal dipole, a sloper, or an inverted-vee antenna (which is how I used it) The dipole elements are each 51 ft long The feedline can be either 300- or 450- twin lead For 300- cases, use 29 ft of line, and for 450- line, use 34 ft One end of the parallel transmission line is connected to the antenna, and the other end is connected to a length of 50- coaxial

The spherical mirror model can be used to develop a simple equation for spherical mirrors You must use the paraxial ray approximation, which states that only rays that are close to and almost parallel with the principal axis are used to form an image Using this, in combination with the law of reflection, leads to the mirror equation, relating the focal length, f, object position, do, and image position, di, of a spherical mirror Mirror Equation

Hubble Trouble In 1990, NASA launched the Hubble Space Telescope into orbit around Earth Hubble was expected to provide clear images without atmospheric distortions However, soon after it was deployed, Hubble was found to have a spherical aberration In 1993, corrective optics, called COSTAR, were installed on Hubble to enable it to produce clear images

The reciprocal of the focal length of a spherical mirror is equal to the sum of the reciprocals of the image position and the object position

34 Given:

When using this equation to solve problems, it is important to remember that it is only approximately correct It does not predict spherical aberration, because it uses the paraxial ray approximation In reality, light coming from an object toward a mirror is diverging, so not all of the light is close to or parallel to the axis When the mirror diameter is small relative to the radius of curvature to minimize spherical aberration, this equation predicts image properties more precisely

Adding and Subtracting Fractions When using the mirror equation,

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Creating PDF files in ASP. NET Core | Software Engineering
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