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By W. V. T. Rusch

ISBN-10: 0126034508

ISBN-13: 9780126034509

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I n a homogeneous medium the geometrical rays are straight lines. 4. It is evident from Eqs. 3-24) that the geometrical optics field vectors Εό and Ho are perpendicular to each other and lie in the geometrical wave fronts. Thus the geometrical optics field is T E M . 5. 31-4) Consider a differential section dSi of a wave front Si, formed by the intersection of a narrow bundle of rays with Si (Fig. 6). The FIG. 6. Tube of geometrical rays. 3 25 GEOMETRICAL OPTICS bundle is sufficiently narrow that there is no first-order variation of intensity transverse to the bundle.

If the surface is finite, a necessary but not always sufficient condition for * A stationary point is defined in this context such that the derivative of the phase of the integrand with respect to the integration variable(s) is zero [cf. Eq. 222-5)]. ** For example, the geometrically scattered field from a hyperboloid is derived from the surface integral by Rusch [7]. 54 II EQUATIONS OF THE ELECTROMAGNETIC FIELD a stationary point to exist is that the field point be many wavelengths from the surface.

The asymptotic expressions from which geometrical diffraction is derived are not valid close to a shadow-light boundary. , —6 dB below, the value predicted from geometrical optics alone. This result agrees very closely with the integral result in Fig. 21. REFERENCES 1. Born, M . , "Principles of O p t i c s , " C h a p t e r 3, Pergamon Press, New York, 1959. 2. Keller, J . , T h e geometrical theory of diffraction. Proc. Symp. , Eaton Electron. Res. , Montreal, Canada, June 1953. 3. Keller, J .

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Analysis of Reflector Antennas by W. V. T. Rusch

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