While I was reading an article about diffraction of light on

[peterpang1994]

While I was reading an article about diffraction of light on Wikipedia(http://en.wikipedia.org/wiki/Diffraction), I had some doubts about it.

On the formalism of the angular position of the first minima, it assumes that the light from a source located at the top edge of the slit interferes destructively with a source located at the middle of the slit, when the path difference between them is equal to λ/2. Similarly, the source just below the top of the slit will interfere destructively with the source located just below the middle of the slit at the same angle. Therefore, (d/2)sinθ=λ/2, dsinθ=λ (1), where θ is the angular position of the first minima.

I wonder if I changed the assumption to assumes that the light from a source located at the top edge of the slit interferes CONSTRUCTIVELY with a source located at the middle of the slit, when the path difference between them is equal to λ/.I will get dsinβ=2λ (2), where β is the angular position of the first maxima. I know that equation (2) is wrong, the correct equation should be dsinβ=3λ/2. My question is why we can't formulate the equation as straight forward as we did in formulating the equation for the interference pattern formed in Young's experiment.

Any reply would be great!

 

[Valerie Park]

When you assume constructive interference for the light from the top edge of the slit and the middle of the slit, the path difference between them is not only λ/2, but also λ. This means that the path difference between them can also be 3λ/2, and this is why the equation for the first maxima has to be formulated as dsinβ=3λ/2. In Young's experiment, the assumption is that the sources located at the top and bottom of the slit interfere destructively, so the path difference between them is always λ/2 and thus the equation can be formulated as dsinθ=λ/2.