When two wave sources are driven in phase, the centre-line between the 2 sources

Question

When two wave sources are driven in phase, the centre-line between the 2 sources is a line of constructive interference. If we change the phase of one of the sources, the angle of this constructive interference line will change (diagram below). Assuming you are at a distance, r, that is much greater than the distance, d, between the sources: What is the equation for the angle of this line of constructive interference as a function of the relative phase of the sources, the distance between the sources and the wavelength? How could this effect be used for something?

Explanation / Answer

a)    The equation is :

d * sin(theta) = n * lambda

=> d * (r/D) =   n * lambda

=>   d   =   (Dn/r) * lambda

b)    This effect can be used to determine wavelength of a monochromatic light source .

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