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Saturday, October 4, 2014

One Path Too Many

Fresnel's Zone radius,

B2+r2+C2+r2CB=A

B2+r2+C2+r2=A+B+C

B2+r2C2+r2=A+B+C2C2+r2

B2C2=(A+B+C)(A+B+C2C2+r2)

B2C2=(A+B+C)22(A+B+C)C2+r2

C2+r2=(A+B+C)2B2+C22(A+B+C)

r2=((A+B+C)2B2+C2)24C2(A+B+C)24(A+B+C)2

={(A+B+C)2B2+C2+2C(A+B+C)}.{(A+B+C)2B2+C22C(A+B+C)}4(A+B+C)2

={(A+C)2+2B(A+C)+C2+2C(A+B+C)}.{(A+C)2+2B(A+C)+C22C(A+B+C)}4(A+B+C)2

r2={A(A+2C)+2C(A+2C)+2B(A+2C)}A{A+2B}4(A+B+C)2

r2=A{A+2B}{A+2C}{A+2(B+C)}4(A+B+C)2

r=A{A+2B}{A+2C}{A+2(B+C)}2(A+B+C)

when  A  is small,

rA(2B)(2C)(2(B+C))2(B+C)

r2ABCB+C,A=λ2

rλBCB+C

The carrier destructively interfered.  Why would there be alternate paths, other than the straight line?