Hi everyone. I am having some difficulty understanding the formulas of single slit diffraction and diffraction gratings. This is partly because the formulas that I have been given in class do not reflect what I have found online entirely.(adsbygoogle = window.adsbygoogle || []).push({});

As we know, the formula forsingle slit destructive interferenceis:

dsinθ = mλ where m = 1,2,3 etc. because there is not destructive interference at the zeroth order.

However, in class we were also told that there is a formula forsingle slit constructive interferenceas well:

dsinθ = (m+1/2)λ where m = 0, 1, 2, 3 etc. When I look online and look into other physics books, I do not find this formula forsingle slit constructive interference. In fact, I only find the formula related to destructive.

My next confusion is with the formulas ofdiffraction grating

The formula I learned forconstructive interferencein this case is:

dsinθ = mλ which is perfectly fine.

But in class, I was also given a formula fordestructive interference:

dsinθ = (m+1/2)λ

I learned from previous discussions with the great people on these forums that dsinθ = (m+1/2)λ is not applicable for destructive interference on diffraction grating. Following up on this, the interference pattern for diffraction grating, compared to double slit, is:

As we can see, for double slit, the area in which destructive interference entirely occurs is in the middle of two bright orders. For that reason,dsinθ = (m+1/2)λmakes sense to me. But clearly that is not the case for diffraction grating, because there are numerous points between the bright orders where complete destructive interference occurs.

EDIT: I found a site (http://www.pa.uky.edu/~cao/NOTES-SPRING06/ch24_lecture-2-S06.pdf) that saiddsinθ = (m+1/2)λdoes apply for destructive interference in diffraction grating. This is beginning to add more confusion..

Is anyone able to help me clear this confusion or misunderstanding. Are the formulas that I mentioned I am confused about truly not applicable to the type of diffraction described?

Thank you.

Side note: I just watched a couple more resources and I found that dsinθ = (m+1/2)λ for constructive interference of single slit diffraction is anapproximate. I think that is good enough to clear that confusion, but my confusion of the diffraction grating destructive interference still resides.

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# B Single Slit and Diffraction Grating Formulas

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