Q: The “inversion theorem” for Fourier transforms states that /
The “inversion theorem†for Fourier transforms states that Use this to determine A˜(k), in Eq. 9.20, in terms of f (z, 0) and f˙(z, 0).
See AnswerQ: A plane wave traveling through vacuum in the z direction encounters a
A plane wave traveling through vacuum in the z direction encounters a perfect conductor occupying the region z(( 0, and reflects back: / (a) Find the accompanying magnetic field (in the region z < 0)....
See AnswerQ: Suppose / (This is, incidentally, the simplest
Suppose / (This is, incidentally, the simplest possible spherical wave. For notational convenience, let (kr − ωt) ≡ u in your calculations.) (a) Show that E obeys all four of Maxwell’s equations, in...
See AnswerQ: Light of (angular) frequency ω passes from medium 1,
Light of (angular) frequency ω passes from medium 1, through a slab (thickness d) of medium 2, and into medium 3 (for instance, from water through glass into air, as in Fig. 9.27). Show that the trans...
See AnswerQ: A microwave antenna radiating at 10 GHz is to be protected from
A microwave antenna radiating at 10 GHz is to be protected from the environment by a plastic shield of dielectric constant 2.5. What is the minimum thickness of this shielding that will allow perfect...
See AnswerQ: Light from an aquarium (Fig. 9.27) goes
Light from an aquarium (Fig. 9.27) goes from water / through a plane of glass / into air (n = 1). Assuming it’s a monochromatic plane wave and that it strikes the glass at normal i...
See AnswerQ: According to Snell’s law, when light passes from an optically dense
According to Snell’s law, when light passes from an optically dense medium into a less dense one (n1 > n2) the propagation vector k bends away from the normal (Fig. 9.28). In part...
See AnswerQ: Obtain Eq. 9.20 directly from the wave equation,
Obtain Eq. 9.20 directly from the wave equation, by separation of variables.
See AnswerQ: Consider the resonant cavity produced by closing off the two ends of
Consider the resonant cavity produced by closing off the two ends of a rectangular wave guide, at z=0 and at z=d, making a perfectly conducting empty box. Show that the resonant frequencies for both T...
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