A dome made of material with epsilonr 24 is to be installed

A dome, made of material with epsilon_r = 2.4 is to be installed over a radar system that operates at 5.5 GHz. The material is only available in 1/4 inch, 1/2 inch, 3/4 inch and 1 inch thickness. Determine which thickness material will provide the best dome. Using the thickness selected in part A, what percentage of power will be transmitted through the dome? Using the thickness selected in part A, determine the percentage of power that will be transmitted through the material at the following frequencies.

Solution

Dielectric constant is also called relative permitivity. So here the permitivity is takenrelative to vaccum(k=1). And with respect to vaccum, metals are the most polarizable material. So it conducts totally.

The propagation and reflection of TM light in a subwavelength slit in a real metal are analyzed. The results for the real metal differ significantly from that of a perfect electric conductor due to the existence of surface plasmons. As the slit becomes narrower or the relative permittivity of the metal becomes less negative, the effective index of the mode in the slit increases and the amplitude and phase of the reflection of the mode at the free-space boundary are modified. To see the influence of these changes for the real metal, it is shown that significant changes in the film thickness, greater than a factor of 2 for noble metals in the visible spectrum and 20nm slits, are required to maintain the Fabry-Perot resonance at a constant wavelength as the relative permittivity is varied.