314 BELL SYSTEM TECHNICAL JOURNAL 



incidence, the reflection is perfect, and the coeflicient of reflection is said to 

 be unity. Bearing in mind that H, = e(vxE) before reflection and H^ = 

 e( — V X — E) after reflection, it is evident that the direction of the magnetic 

 intensity has been unchanged by the process of reflection and that the re- 

 sultant magnitude at the surface of the metal is | //j | + | ^r I = 2 | ^ | . 

 Thus we see that, at the moment of reflection from a metallic surface, the 

 resultant electric force vanishes and the resultant magnetic force is doubled. 



The reflection of waves at the end of the line naturally gives rise to two 

 oppositely directed wave trains. This is a well-known condition for standing 

 waves. Though a complete discussion of standing waves calls for the math- 

 ematical steps taken in Section 3.6, there are certain qualitative results that 

 may be deduced from relatively simple reasoning. Some of these deductions 

 will be made in the paragraphs that follow. 



If an observer, endowed with a special kind of vision for individual lines 

 of force, were to be stationed at various points along a lossless transmission 

 line as shown in Fig. 6.2-5, he would observe a variety of phenomena as 

 follows. Near the reflector he would observe a waxing and waning of lines 

 of force, both electric and magnetic, corresponding to the arrival of crests 

 and hollows of waves. Also he would observe a similar waxing and waning 

 corresponding to waves leaving the reflector. The sum of the two waves 

 would give rise at the conducting barrier to a resultant electric intensity of 

 zero and to a corresponding magnetic intensity that would oscillate between 

 limits of plus or minus 2H. Since it is the magnetic component that is the 

 the more evident near the barrier, this region would appear to the observer 

 much like the interior of a coil carrying alternating current. 



If the observer were to pass along the line to a point one-eighth wave- 

 length to the left of the reflector, the distance up to the reflector and back 

 would then be a quarter wave and he would then find that at the moment 

 that a wave crest (maximum intensity) was passing on its way toward the 

 reflector a point on the wave corresponding to zero intensity would be re- 

 turning from the reflector. Adding the corresponding electric and magnetic 

 intensities at this point, he would observe that the electric intensity would 

 not always be zero but instead it would oscillate between limits of plus or 

 minus \/2 E. Similarly the corresponding magnetic intensity would no longer 

 oscillate between limits of plus or minus 211, but instead it would never reach 

 limits greater than plus or minus \/2 //. Thus at this point the electric and 

 magnetic comj)onents would have the same average intensity. 



If the observer were to move farther along the line, stopping this time at a 

 distance of one-fourth wavelength to the left of the metal plate, the total 

 electrical distance to the barrier and back again would be a half wave- 

 length and he would now fmd that at the time a crest passed on its way 

 toward the reflector a hollow (maxiimini negative intensity) would be pass- 



