IMPEDANCE CONCEPT AND APPLICATION 41 



in the other the magnetic field is so disposed. The former wave may 

 be called transverse electric and the latter transverse magnetic. The 

 product of the corresponding radial impedances of these waves is 

 equal to the square of the intrinsic impedance. Hence if one wave 

 is a low impedance wave (as compared to the intrinsic impedance), 

 the other is a high impedance wave. Under the usual engineering 

 conditions these waves are unmistakably different in air, although 

 this distinction disappears in metallic media. It must be pointed 

 out, however, that for micro-waves the dimensions of the shield may 

 be comparable to the wave-length, in which case the radial impedances 

 may be of the same order of magnitude. 



In the above discussion we have supposed that the line source was 

 on the axis of the shield. If it is not, it is possible to represent the 

 actual source by means of an equivalent system of sources along the 

 axis and calculate the shielding effect. The latter is different for 

 cylindrical waves of different orders. This will result in somewhat 

 different shielding for different positions outside the shield. Ordi- 

 narily, however, the difference is not large enough to be considered in 

 practical problems. 



Spherical Waves 



A small coil carrying an alternating current will give rise to a trans- 

 verse electric spherical wave and a small condenser to a transverse 

 magnetic wave. Consider a shield concentric with the coil or the 

 condenser. In the shield the radial impedance is yluojjjg, again ex- 

 cepting very low frequencies. In air the radial impedance of the 

 outward bound electric wave is ^^ fw/xr and that of the internal wave 

 ^iuij.r. The corresponding impedances of transverse magnetic waves 

 are l/iooer and l/iwer. The conditions for reflection and shielding are 

 substantially the same as in the case of cylindrical waves. Some 

 quantitative difference results from the inequality of the radial imped- 

 ances in opposite directions. 



Plane Waves 



The next example of uniform linearly polarized plane waves is par- 

 ticularly well known. ^"^ When the boundary between two media coin- 

 cides with an equiphase surface of the impinging wave, the formulae 



13 Equations (9), (10). 



^* The general formulae for the reflection and transmission coefficients have been 

 obtained by T. C. Fry on the basis of the Maxwell theory in his paper " Plane Waves 

 of Light II," published in the Journal of the Optical Society of America and Review 

 of Scientific Instruments, Vol. 16, pp. 1-25 (1928). The earliest formulae are prob- 

 ably due to A. Cauchy, who obtained them from the "elastic solid" theory of light 

 waves. 



