- #1
Abu
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.
As we know, the formula for single slit destructive interference is:
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 for single slit constructive interference as 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 for single slit constructive interference. In fact, I only find the formula related to destructive.
My next confusion is with the formulas of diffraction grating
The formula I learned for constructive interference in this case is:
dsinθ = mλ which is perfectly fine.
But in class, I was also given a formula for destructive 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)λ makes 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 said dsinθ = (m+1/2)λ does 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 an approximate. I think that is good enough to clear that confusion, but my confusion of the diffraction grating destructive interference still resides.
As we know, the formula for single slit destructive interference is:
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 for single slit constructive interference as 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 for single slit constructive interference. In fact, I only find the formula related to destructive.
My next confusion is with the formulas of diffraction grating
The formula I learned for constructive interference in this case is:
dsinθ = mλ which is perfectly fine.
But in class, I was also given a formula for destructive 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)λ makes 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 said dsinθ = (m+1/2)λ does 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 an approximate. 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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