What is the concept behind Diffraction, “n”, Finding Dark/Bright Spots

I used the following youtube video to help me learn about the concept of diffraction but still could not make sense of my lecture notes:

http://ift.tt/1eKo7HI (All 4 parts)

SINGLE SLIT DIFFRACTION

In order to find the minima the following formula is used, a*sinθ=n*λ, what does "n" exactly mean and how does the order relate to the dark/bright spots on the screen, (a=slit width,λ=wavelength).

The extra distance travelled by the rays = a/2*sinθ, while the phase difference is always λ/2 (learned via youtube video above)

So, a/2*sinθ=λ/2 from which we find the formula a*sinθ=n*λ

Sinθ can be replaced by x/D, where x is the distance from the central max to the desired Max/Min and "D" is the distance from the screen to the slit.

1st Dark Spot on the screen: a/2*x/D=λ/2, what does "n" equal here, is it 1? and does a*sinθ=n*λ apply?

1st Max Spot: a/3*x/D=λ/2 (found from video), what does "n" equal here and does a*sinθ=n*λ also apply here.

How will i know in a question if i need to find a Max or a Min? As i can’t seem to find the relationship between the order and the dark/bright spots on the screen.

Are the following correct:

Central Max: n=0
1st Dark: n=1
1st Max: n=2
2nd Dark: n=3

and then does a*sinθ=n*λ need to be applied to find the desired solution? but i can’t apply it to the Max or the Min, for example 1st Dark Spot is a/2*x/D=λ/2 (learned from the video), how do i get this from a*sinθ=n*λ and what does "n" equal in this case for dark spot and the same for the 1st Max, 2nd Dark, 2nd Max etc.

Also in my notes i see a graph of intensity(y-axis) and sinθ(x-axis) with values such as λ/a, 2λ/a, what do they mean? i know that a*sinθ=λ where sinθ=λ/a is from the 1st Dark Spot, but then i have 2λ/a where sinθ=2λ/a but what does that represent?

I see it may come from a*sinθ=n*λ where the "n" value is number 2 but how do i know what the "n" number represents because i can’t figure out if they are dark or bright spots. Also if λ/a is a bright spot? then 2λ/a would represent the 1st max? but how can that be when it is a/3*x/D=λ/2

As you can see i have a basic understanding of the science behind what is happening but i need to understand the thinking behind the use of the formulas to find the dark/bright spots and their relationship with "n" which is my main issue. Since their is a set formula for minima the one which i have shown above i want to understand how to use it to find the dark spots but since it applys to minima i assume there must be one for maxima and i hope to understand how the formula can be used to find the bright spots and the relationship with "n" in all of this.

DOUBLE SLIT DIFFRACTION

With double slit difraction the extra distance travelled for the following is:

1st Max: 1λ
2nd Max: 2λ
3rd Max: 3λ

1st Dark: λ/2
2nd Dark 3/2*λ

where for example to find 1st dark you have d*sinθ=λ/2, is there a general formula in this case to find max or min which also involves the use of "n" to find the bright or dark spots.

CIRCULAR APETURE AND DIFFRACTION GRATING

For circular apeture, is there anything beyond sinθ=1.22*λ/a(diameter of opening) and R(radius)=1.22*λ*D/a and do these formulas help me find the max and minima? use of "n"? etc

Diffraction grating, d*sinθ=m*λ what is "m" and how do i know which value for "m" corresponds to a dark or bright spot when i am trying to find one. For example:

extra distance travelled for 1st max: λ and 2nd max: 2λ in this case does that mean for the 1st max m=1 and second max m=2 and then i apply it to the formula d*sinθ=m*λ to find the solution i require?

Sorry for the lengthy question wanted to make sure i fully understand what is happening, will appreciate your time and patience.

Thank you very much for any help guys.

http://ift.tt/1eKo9j0

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