proof of equation of delta phi in 2 ray model???

[moonnightingale]

Can u give me proof of two equations in two ray model

delta phi = 4pixhtxhr/(lamdaxd)

and other equation x+x'-l

Equations also attached

 

[bulx]

Your second picture has the answer.

The lowest right triangle formed with (x + x') as hypotenuse, and with (ht +hr) and d as perpendicular sides gives

x + x' = sqrt ( (ht +hr)^2 + d^2 )

Another right angled triangle is the top one with l as hypotenuse and d and ht -hr as perpendicular sides. This gives

l = sqrt ( (ht-hr)^2 + d ^2 )

subtracting gives you the reqd result.

And the second results comes from using (1 +x )^n = 1 +nx when x << 1. Here we have x = ((ht ± hr)/d)^2

- b