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

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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