Chapter 9: Q9.22P (page 417)
Calculate the reflection coefficient for light at an air-to-silver interface at optical frequencies.
Short Answer
The reflection coefficient for light at an air air-to-silver interface is .
Chapter 9: Q9.22P (page 417)
Calculate the reflection coefficient for light at an air-to-silver interface at optical frequencies.
The reflection coefficient for light at an air air-to-silver interface is .
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Get started for freeShow that the mode cannot occur in a rectangular wave guide. [Hint: In this case , so Eqs. 9.180 are indeterminate, and you must go back to Eq. 9.179. Show that is a constant, and hence—applying Faraday’s law in integral form to a cross section—that , so this would be a TEM mode.]
Consider a rectangular wave guide with dimensions . What TE modes will propagate in this waveguide if the driving frequency is ? Suppose you wanted to excite only one TE mode; what range of frequencies could you use? What are the corresponding wavelengths (in open space)?
In writing Eqs. 9.76 and 9.77, I tacitly assumed that the reflected and transmitted waves have the same polarization as the incident wave—along the x direction. Prove that this must be so. [Hint: Let the polarization vectors of the transmitted and reflected waves be
prove from the boundary conditions that .]
Suppose
(This is, incidentally, the simplest possible spherical wave. For notational convenience, letin your calculations.)
(a) Show that obeys all four of Maxwell's equations, in vacuum, and find the associated magnetic field.
(b) Calculate the Poynting vector. Average S over a full cycle to get the intensity vector . (Does it point in the expected direction? Does it fall off like , as it should?)
(c) Integrate over a spherical surface to determine the total power radiated. [Answer:]
By explicit differentiation, check that the functions , , and in the text satisfy the wave equation. Show that and do not.
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