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M(:,m)=getframe;
end
movie(M,20)

Compare the spatio-temporal profile of the resultant to that for a single wave
(i.e., set x2 = 0).

6.7.2 Addition of Two Electromagnetic Waves
In many practical instances, we are faced with the problem that two em
waves originating from the same source, but following different spatial
paths, meet again at a certain position. We want to find the total field at this
position resulting from adding the two waves. We first note that, in the sim-
plest case where the amplitude of the two fields are kept equal, the effect of
the different paths is only to dephase one of the waves from the other by an
amount: ∆φ = k∆l, where ∆l is the path difference. In effect, the total field is
given by:

E ( = E cos[ω t + φ ] + E cos[ω t + φ ] (6.76)
t)
tot. 0 1 0 2
where ∆φ = φ – φ . This form is similar to those studied in the addition of two
2
1
phasors and we will hence describe the problem in this language.
The resultant phasor is

˜
E ˜ = E + E ˜ (6.77)
tot . 1 2

Preparatory Exercise

Pb. 6.43 Find the modulus and the argument of the resultant phasor given
in Eq. (6.74) as a function of E and ∆φ. From this expression, deduce the rela-
0
tion that relates the path difference corresponding to when the resultant pha-
sor has maximum magnitude and that when its magnitude is a minimum.
The curve describing the modulus square of the resultant phasor is what is
commonly referred to as the interference pattern of two waves.

6.7.3 Generalization to N-waves
The addition of electromagnetic waves can be generalized to N-waves.

© 2001 by CRC Press LLC