To examine the conditions under which the approximations of Eq. (9.23) are valid:

(a) Apply the law of cosines to triangle S₁S₂P in Fig. 9.11c to get

(b) Expand this in a Maclaurin series yielding

(c) In light of Eq. (9.17), show that if (r₁ - r₂) is to equal α sin θ, it is required that r₁ >> α²/λ.

Fig. 9.11c 

Transcribed Image Text:

(9.23) að 271/2 12 |sin 0 +