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Fig5_12 - 156 Chapter5 Geometrical Optics 5.2.3 Thin Lenses...

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Unformatted text preview: 156 Chapter5 Geometrical Optics 5.2.3 Thin Lenses Lenses are made in a wide range of forms; for example, there are acoustic and microwave lenses. Some of the latter are made of glass or wax in easily recognizable shapes, whereas others are far more subtle in appearance (see photo). Most often a lens has two or more refracting interfaces, and at least one of these is curved. Generally, the nonplanar surfaces are centered on a common axis. These surfaces are most frequent— ly spherical segments and are often coated with thin dielectric films to control their transmission properties (see Section 9.9). A lens that consists of one element (i.e., it has only two refracting surfaces) is a simple lens. The presence of more than one element makes it a compound lens. A lens is also classi- fied as to whether it is thin or thick—that is, whether or not its thickness is effectively negligible. We will limit ourselves, for the most part, to centered systems (for which all surfaces are rotationally symmetric about a common axis) of spherical sur— faces. Under .thesé restrictions, the s1mple lens can take the A lens for short-wavelength radiowaves. The disks serve to reirari forms shown in Hg 5'12‘ these waves much as rows of atoms retract light. (Photo courtesy m Lenses that are variously known as convex, converging, or Society of America) positive are thicker at the center and so tend to decrease the radius of curvature of the wavefronts. In other words, the wave converges more as it traverses the lens, assuming, of course, that the index of the lens is greater than that of the media in which it is immersed. Concave, diverging, or negative lenses, on the other hand, are thinner at the center and tend to advance that portion of the wavefront, causing it to diverge more than it did upon entry. Thin-Lens Equations : R, = a: Return to the discussion of refraction at a single spherical R2 > 0 interface, where the location of the conjugate points S and P is ’ fir given by Planar concave ”—1 + 3 : ——("’2 _ n‘ [5.8] SO Si R g R1>0 R2 > 0 When so is large for a fixed (n2 - n1 ) / R, s, is relatively small. its, As so decreases, s,- moves away from the vertex; that is, both 9,» “misc“ ”en's“ COI‘IVCX concave and 6‘, increase until finally so = f0 and s,- = 00. At that point, ”1/5“ = (n? ; filo/R so that If SO gets any smaller, Si “Ill-1 have Figure 5.12 Cross sections of various centered spherical in [0 b6 nagatlve, 1f EQ- (5-3) 13 t0 h01d- In other words, lhfi 1mage lenses. The surface on the left is #1 since it is encounteredi ‘fi' becomes Vil’tual (Fig. 5.13). Its radius is R1. (Photo courtesy of Melles Grist.) ...
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