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Three parallel rays with differing path lengths

Imagine three coherent monochromatic waves as depicted in the image. Say we are interested in the interference at a very distant point P (not depicted). As one can see, B will interfere destructively with A and C whereas A and C will interfere constructively with each other. My question is: what intensity will we see at P? Will there be brightness, darkness or something in between? My guess is that we will see the constructive interference between A and C. On the other hand, one might not see anything because B has cancelled both A and C, so they can't even interfere with each other? What is it going to be?

playdis
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    As posed, your question cannot be answered. The green lines presumably represent rays, while the dotted lines presumably represent wavefronts. No aperture width is specified, and the location of P relative to the aperture is specified. You should look up single-slit diffraction and Fraunhofer diffraction. – S. McGrew Dec 26 '18 at 16:32

1 Answers1

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Let the amplitude of the waves from each of the sources at the observation position be $A$.

If there is no difference in path then the resultant amplitude at the observation position is $A+A+A=3A$ and the intensity of this zero order fringe is $9A^2$.

If the path difference between adjacent sources is $\frac{\lambda}{3}$ then the resultant amplitude is zero.

$A\sin(\omega t)+A\sin(\omega t+\frac{2π}{3})+A\sin(\omega t+ \frac{4π}{3}) =0$.

For the $\frac{\lambda}{2}$ path difference that you asked about the resultant amplitude is $A-A+A=A$ with an intensity $A^2$.

$A\sin(\omega t) +A\sin(\omega t+\pi)+A\sin(\omega t+ 2\pi) = A\sin(\omega t) $.

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This answer has much more detail about multiple source interference (including three source) and information as to how you could use phasors to predict what the interference pattern might look like.

Farcher
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