Problem with the two slit experiment, Observing later

A correction to my prior post...a photon has relativistic mass, not invariant
mass. LL

This post has been edited by Laserlight on Jan 16 2007, 06:14 AM

Hi TRoc,

Here..
http://hyperphysics.phy-astr.gsu.edu/hbase...sinslit.html#c1
yet again it is the difference in path length between the left hand side and the right hand side that causes constructive/destructive interference. The superior person would doubtless attempt some sort of integration of the path lengths over the width of the slit .. which would give us the finer details (logs,curlies and spirals) .. the less superior person (like me) gives in to idleness and accepts the left/right path difference is close enough to establish the 'path difference' principle.

No. Sorry.

[ quote=TRoc ] when the path lengths are altered, is there a time difference of incidence at the screen? That is, from your "new source" (the slit), do all the "adjusted" path lengths travel at the same velocity?[ /quote ]

As far as I know that pretty much defines the DSE problem .. the thing that is to be explained .. the thing Feynman gave up on .. the thing none of us are even close to starting to attempt to explain.

My reason for failing to 'commit' over the counts in between the regions of destructive interference was that I didn't want to get into (another) dispute with Good Elf about hidden variables. Hopefully we may agree the result is that the probability of detecting a photon is given by k (cos(2 pi delta/wavelength))^2 .. where delta is the path difference. If a near field analysis is attempted then it will be important to integrate over the width of each slit .. but the principle remains the same.
Best wishes,
-C2.

Light refraction is accelerated by the size of the refraction index or ''slit'' because of the light being forced through a tiny space.

Pushing air through your nose would accelerate much much faster than say trying to push air through your mouth.

It all depends on size, usually size = greater output or input this is reverse in lights case.

Hi Laserlight,

The quantum energy "pulse" is not a qubit. A qubit is the superposition of the "three possible states" a one a zero and a one and a zero (the superposition).

Just discussing energy for a tad... E = MC²
Energy is always referenced to a "zero level" ... what is this zero level? How do I measure it? IMHO the derivation of energy is subject to a "constant of integration", unless you measure relative to some frame it is "meaningless", energy is not "absolute". Your "relativistic mass" is difficult to define in a system that has not been measured. Einstein warned about this...

"Concentrated energy"... what is this? ... energy is defined as capacity for doing work nothing more... you speak as if it was a "liquid" or "fluid". It is ∫F.ds where F = Force and ds = displacement. You are probably referring to EM sources?? This is not "energy" as such. The ability to stretch a rubber band is "energy" because it is F.s but you can't "concentrate" it. It is more abstract than that. What if we think this way... spacetime curvature is "mass" (symmetric) and spacetime spin is electromagnetism (anti-symmetric). Their interdependence is "something like" this...

Click to enlarge...

The symmetric part is the "curvature" on the surface and the "spin" keeps it "open". That is the way Einstein thought of it in one of his "Unified Field Theories" of course it might get a little more complicated than this "today" but all forces will ultimately be "one" (we hope). Notice though "electromagnetism" (somehow) produces the mass and not the other way around. This we see with all fermions derived from bosons (photons). Notice also this "Universe" is more than the "surface".... "what lies beneath" is very important. And this is a lower dimensional "analog".

What say you Laserlight? (other comments welcome)

Cheers

This post has been edited by Good Elf on Jan 16 2007, 03:17 PM

Hi ChaosTheory,

Naturally we need to test your shnozzle theory..
There's a flock of diffraction things here ..
http://hyperphysics.phy-astr.gsu.edu/hbase...ffracon.html#c1
The closest (simplified) version to shnozzle diffraction looks to be this
http://hyperphysics.phy-astr.gsu.edu/hbase...cirapp2.html#c2
Can you shnozzle the same result .. or something similar?
I think Huygens is the one to blame ..
http://en.wikipedia.org/wiki/Huygens_principle
Does that help?

Best wishes,

-C2.

Hi all,


C2, First, you have quoted LL, and attributed this to me:

"QUOTE (TRoc) Can you explain to me how diffraction works? Why does light going thru a slit spread and why does the width of the slit affect the amount of spread induced? "

and

"QUOTE (TRoc) Would you say that the slit(s) are functioning like lenses with an index of refraction? "

so, you should answer to him.

BTW, the link you gave in your "attempt" to explain "how diffraction works" doesn't use the word "path length" at all. You also strongly claimed to "not need the slit width" parameter, yet the link you gave to "make your point" uses it. So, basically, you are saying you have no idea, correct?


Your "huge" answer was at the same level; I have no idea what it is that you really want to say. It definitely is not an "answer".

[ quote=TRoc ] when the path lengths are altered, is there a time difference of incidence at the screen? That is, from your "new source" (the slit), do all the "adjusted" path lengths travel at the same velocity?[ /quote ]

C2: "As far as I know that pretty much defines the DSE problem .. the thing that is to be explained .. the thing Feynman gave up on .. the thing none of us are even close to starting to attempt to explain. "

?? ??

"Pardon me sir, will you kindly step out of the way; I'm in the middle of doing what you say can't be done".

The "triple vague negative": this may set a new record! "not even close" to "starting" to "attempt" to explain something. What you are describing sounds like "a pre-thought" to me, not the pages of "words" that fill this thread. Just speak for yourself, please.

I think in much the same way that you "exposed" your particle beliefs well into this thread, we have now a second disclosure: you are a faithful, and die-hard believer in ________, and you won't be swayed by any "proof", or "logic", those things died with Feynman! "now here this": The Copenhagen "surrender" will now be postponed until after Feynman. Hooray!!!


The far field method requires the "empty space" of the slit width the same as the near field method. They both use the slit as the KEY to shifting geometry, so that the angles change, and the path lengths change. Diffraction is the "at the slit" explanation, there is no getting around it: arbitrary points across the slit width = ad hoc = you can not explain the phenomenon completely with this method.


regards,

T.Roc



This post has been edited by TRoc on Jan 16 2007, 04:32 PM

Good Day EVERYONE!
I have spent 2 days catching up. I have 3 pages of quotes from all of you which leads to this presentation.
© is a constant.
Therefore, the distance, (l), that light travels is a constant. It has always been a constant.
-------------------------------------

Experiment # 1
Get a pack of sticky circles from your office supply store.
Mark six of them with a big “E”. It represents Energy in all its possible forms.
The circle represents the smallest possible scale at which energy is contained. It is the Planck Area. It is the smallest distance that energy can travel. Your circles will look like the following arrangement. (energy_nodes)

You cannot put the Planck scale energy nodes any closer than shown. They must be separated by a “nul” node of no energy. Therefore, the minimum total surface area is 24 Planck units.
----------------------------------------

Experiment # 2
Get an orange that has a circumference of those six circles. Stick your circle on the orange.
You have now proven that the minimum size of a Planck Sphere is 24,(l) in area and that there can only be six Planck size ENERGY in a Planck size sphere.
Play with it. You will be able to find all kinds of quantum geometry relationships, like Hex. packing.
--------------------------------

Experiment # 3
Now, lets go to 3d. From the 2d arrangement, we will take one ENERGY node and 3 “nul” nodes and place them on the X plane. Then one ENERGY node and 3 “nul” nodes and place them on the Y plane. Then one ENERGY node and 3 “nul” nodes and place them on the Z plane.
Mathematically, Good Elf says, “Please note that this is a spatially distributed complex function and is represented by a complex plane 6 dimensional function (x,y,z,ix,iy,iz) in the real most general three dimensional case.”
To me, it is just the real location of the 2d energy in a 3d configuration.

That will make a total of 6 energy nodes and 18 “nul” nodes.
Here is my picture of one energy node and 3 “nul” nodes. (energy_nodes_2)

This will make a 3d sphere that has 3 energy nodes and 9 “nul” nodes. From the previous 2d energy distribution we can get two (2) 3d spheres that contain 3 energy nodes and 9 “nul” nodes. Each sphere will have a total of 12 nodes.(3d rotation)
How many energy nodes does a proton or a neutron have?
We call them “quarks”.
Do you have a model that can generate “quarks”?
A physicist will quickly point out that the total energy of a proton or a neutron is not the sum of the 3 quarks. There is something else making up the total energy.
How right!
Let’s put the proton into the 3d spacetime configuration that I have worked out, the 12 hex. packing of 12 spheres. There is plenty of room.
12 spheres X 12 nodes = 144 nodes that are available. A proton will only use 12 nodes.




All of the above has been derived for “first principles”. The speed of light is CONSTANT. If you change the speed of light then you have changed the distance, (l), that light must travel. © as a constant depend directly on (l) the distance. It does not depend on the size of (l). Therefore, (l) can be 10^-33 or even 10^-18.



Do you need your quotes?
Laserlight

I don't think that there is evidence that subatomic fundamental particles exhibit
cyclical movement, but I could be wrong about that.
TRoc
that they didn't find the "mathematical" explanation for the chord.
all that was necessary to tweak the whole thing into producing the constant c with any symmetrical pair of values. This is reminiscent of Maxwell's (original) quaternion notation. The symmetries always have an angle, like a matrix, that produces a "unity", in this case, c .
Physics has only looked at this from the "form" of the wave, as it appears.
You just need a starting point (background "noise" of the Universe), and one, expanding, geometrically progressive "measuring stick".
TRoc
More to your question of the "vibration of particles". Just like the "photon", the electron, neutron, and proton are also localized wave centers, and not really "particles". They do have mass, however, and Einstein has worked out the details on the energy, which I'll remind you that is defined by mc^2 = E = hf, where f=frequency, that each of these "particles" posses. The free electons and protons can be used in the S/DSE, with the same results that we have been talking about.
TRoc
We can only measure "note for note" resonance between electrons, and it is called the "photon". The electron has the Compton wavelength (derived one way), and the deBroglie wave (another way). Take c , and divide it by this wavelength, and you get the frequency of the electron c /w = f . This frequency will match its' mass equivalent, figured by m * c^2 . It all ties together, and is rock solid; if you take this away, we have nothing left. It is not "my opinion", it is Physics.
What my model is about is WHY these fundamental vibrations exist in the first place, and HOW the interactions "conserve".
TRoc
You can see the next question is, "how are the electron and proton produced?", and on down the line, as far as chasing "harmonics" from collisions. I would say that the electron is the lowest energy, stable mass, and it is derived as the smallest stable harmonic of the radius of The Cavity (Universe). This equation has been derived already, by Wolff, in his WSM theory, and dubbed "the equation of the cosmos".
Good Elf
the Raman scattering produces at least a part of the galactic redshift; the expansion of the universe is reduced or possibly canceled.
Wick rotation is named after Gian-Carlo Wick. It is called a rotation because when we represent complex numbers as a plane, the multiplication of a complex number by i is equivalent to rotating the vector representing that number by an angle of π/ 2.
When Stephen Hawking wrote about "imaginary time" in his famous book A Brief History of Time, he was referring to Wick rotation.
Why do we need to invent new non-existent particles to explain a phenomenon that has been around for well over a century? I prefer not to view this as "imaginary time" but simply "imaginary extra space" with those "domain walls". This "space" is no more "imaginary" than it is in any other discipline such as electronics for instance and we see it displayed effectively in animations of the time dependent solutions of the Complex Schroinger Wave Equation. Personal preference I suppose but makes more sense to me.
It "travels" to the screen through a series of nodes and anti-nodes already existing in the space
Provided there has been no change in the geometry this second photon encounters the same nodes and anti-nodes on the way to the screen.
but this time the space is resonating like a bell being repeatedly struck at a critical repetition rate of twice the frequency but each successive strike is opposite in phase to the previous strike which correlate to the "UP" phase followed by a "DOWN" phase. In the analogy of the Russian Soldiers ... first with the left foot then with the right foot etc... This "gaits" the photons spatially on their way to the slits
Confused2

if we knew what steered a photon and how it was organised to steer through two paths of different lengths such that it gives the observed result I think we'd have the answer.
Good Elf
The proton is not apparently a completely primitive object and is composed of three fractionally charged "quarks" which have different influences on each other and cannot be separated any great distances from each other before the energy of that separation is sufficient to create a new "quark system"
Quantum Mechanics offers no mechanism for this other than saying that it just happens
Lets all try and break new ground not wear a circular patch on it by going in around in circles.

All that exists is some kind of physical cavity that exists wherever there are anti-nodes and "non-cavity" in between... the nodes. I realize that zephir will say "the ether" but I reject that as a physical medium.
Once again the answer is the ability of empty space to communicate "instantly" throughout the universe and to construct "holographically" these standing waves in the traversed medium (or non-medium... the vacuum). Are these cavities "repeating" the signal or are they resonant to the frequency of the incoming signal? Are they physically real and represent some volumetric element we are unable to detect in our three dimensional space?
The question is how does space "know" to signal ahead and keep everything in step? We know it does this from the Delayed Choice Quantum Eraser Experiment results. Is it because these cavities are really a reflection of the geometry of our "external " universe...
I would say “really a reflection of the geometry of our spacetime.”
I also believe they represent "compact dimensional spaces" that can be excited into existence not by "power" but are the result of events which is actually information in the space.
Where you see chaos and disorder I see an underlying order that is difficult to determine but may be the reason why we experience time itself.
but this summation is derived from "specific" photons of energy...
E = nhf where n is a quantum number and is an integer and this "hf" is the "lowest" quanta of energy. The significance of this is no matter what we do we will not create photons with energy "in between" the very specific frequencies. Thus we have "stationary states"... States that cannot shift even incrementally from their "base" frequency.
There is no passage of time executing in at least one state so without time nothing "dynamic" can occur such as a force for instance which requires the exchange of a "carrier" (that takes time).
Other mechanisms will not fit my model simply because the mechanisms do not address the experimental issues.
Jal
The mechanisms fits my model.
Good Elf One of these days, I’m going to show up on your doorstep with a six pack of beer to clear the air.
As yquantum said, “Where do we go from here?”

Hi GE,

I believe that this can be stated to be maximum energy (1), zero energy (0),
while the superposition is any analog component of energy between zero and
one.

Potential energy represents the stored energy equivalent available
to do work.

Concentrated energy is the mass equivalent potential energy
(invariant energy) at rest. Think about it. Mass is nothing more than
condensed "potential" energy accumulated into some dense concentrated system.
The density of the mass is directly proportional to the amount of gravity it
possesses. The mass equivalence represents the total energy contained and
follows Einsteins E=mc^2 where m=E/c^2.

The total combined energy "displacement" this mass density represents is directly
proportional to its gravitational component. A tablespoon volume of a neutron
star weighs about 2 Million tons (4T pounds) That represents a lot of potential
energy (mass) and a tremendous gravitational spacial displacement.
http://www.news.harvard.edu/gazette/2002/0...quarkstars.html

IMO, spacetime curvature is the "displacement" caused by the potential energy
that mass represents. What is curvature? It is the warping of normal space-time
and follows the ISL relative to the position of the mass generating the
displacement. Energy density should be directly proportional to gravitational
pull. A pound of lead weighs the same as a pound of feathers. Even though their
volumes and total surface areas are different, their relative densities and the
energy equivalence that they represent (displace) are the same. The distribution
of the volume that they displace spreads the gravitational component they
represent over a larger total area, but it is the same equivalent value.

IMO, if you displace space, you "warp" it. The observed result is the curvature of
spacetime.

I think we are saying the same thing from different perspectives. I guess the
question is, "Does warped space represent an extra dimension, or is it just
a deformation of normal space that causes time to slow down relative to
an external point of observation, due to light following the warp curvature rather
than a following a straight line?"

In the case of light, time is stopped, but time is relative to an external observer
who is making a comparison of the same source of light travelling thru normal
space relative to curved space. Light following a curved trajectory takes longer
to negotiate the distance between 2 points relative to light traveling along a
straight line.

Comments, discussion encouraged.
LL

This post has been edited by Laserlight on Jan 16 2007, 05:06 PM

Hi TRoc,

Very sorry about the wrong attribution..

Hopefully there is a reasonably satisfactory description of diffraction here..
http://hyperphysics.phy-astr.gsu.edu/hbase...inslitd.html#c1

Clearly there is a maximum where the pathlength difference is zero or a whole wavelength.

The superior Fresnel analysis gives virtually the same result for the same reason (path length difference) but allows that the phase is not precisely uniform across the slit.

Interference ... diffraction .. phase difference .. pathlength difference .. all part of the same thing.

Are we in agreement this far? (I fear we are horribly not in agreement .. we shall see)

Best wishes,

-C2.


Edit

Yes! << big letters.

This post has been edited by Confused2 on Jan 16 2007, 05:28 PM

Hi TRoc,

Not an ill-founded claim. It we look at the picture of diffraction here
http://hyperphysics.phy-astr.gsu.edu/hbase...inslitd.html#c1
and then at http://www.teachspin.com/instruments/two_s..._combiplot2.gif
hopefully we see that the entire game of the DSE is (or can be) played out where the main diffraction 'humps' from the two slits are overlapping .. provided the two slits are narrow enough to generate wide enough 'humps' we don't need to know anything more about their geometry... the DSE equation (based on path length difference) holds.

Best wishes,
-C2.

Edit .. with regret

I have to offer the suggestion the absence of any link between the effect and precise geometry of either of the slits suggests (to me) that the precise geometry of either of the slits is not the cause of the effect.

This post has been edited by Confused2 on Jan 16 2007, 06:44 PM

Hi C2 and All,

Again the question comes down to the slit geometry interfering with the
arriving coherent photons and causing them to spread according to how
wide the slit is. A narrower slit causes more interference (diffraction)
which causes more spread. The pattern of interference, occuring at the slit,
is projected onto the screen.

Keep in mind that we are talking about a wavelength of ~700 nm, but if
you look at the screen, the light and dark bands are many millimeters apart. We are observing a dark band that has no apparent photon energy
for many thousands of times the wavelength of light we are using.

If you move the screen further away from the slits the light and dark gaps
increase proportionally, just like a projector. It is my contention that each slit acts
like the refraction occurring as light passes thru a lens, just as in the camera
obscura. The phase and mixing interference is produced as the photons are
being diffracted and the light phases are interfering with each other within the
aperature of the slit "lens".

A single slit acts as a new source for the mixed (phased) photons, some have
been interfered with constructively, some destructively, and some pass straight
thru without any phase shift.

Think about a movie projector, if you focus it on a screen and then move the
screen away the image gets larger. There has been no phase mixing of the
photons anywhere but within the nearfield focal plane of the lens,
but the angles between the screen and the lens maintain the same geometrical
relationship.

In the case of 2 slits (the DSE), we are taking a curved 3 dimensional wavefront,
separating it spacially and temporaly across a 2 dimensional barrier, while
allowing 2 separate parts of that 3D wavefront to continue onward thru the slits.

The slits, which act as signal mixing points, offer some time and spacial delays to the
wavefronts (refractive index), and then the mixed, phase delayed 3D wavefronts
expand from each of the new slit sources toward the screen. The advancing
wavefronts have the same phase and timing offsets that overlap as they spread
toward the screen. Keep in mind that the advancing wavefronts are 3D while
the screen is 2D. I mentioned before that if the screen were curved we should
see straight lines representing the projected interference bands, which would
better represent the curved focal plane of the lens action of the slits and the
curved photon wavefront

Added because of your edit:

The path length difference is a function of the diffraction occuring at the slits.
The path length inteference occurs in the slits and is projected onto the screen.

JMHO!

Comments and discsussion welcome.

LL

This post has been edited by Laserlight on Jan 16 2007, 07:19 PM

C2,

I think that you are saying that now, and we are in agreement.


HOWEVER,

you ARE NOT getting it C2. That is why we are asking you IF you can explain it: not because we don't know, but because we can't believe that you do know. Referring us to another diagram does not convince anyone that you do, and neither do any of your statements.

You CAN NOT operate your model, or solve your equation WITHOUT making arbitrary points in which to draw new paths of different lengths from the slit to the screen. These new points ARE equal (or symmetric) distance apart, which CREATES the relationship of whole or half wavelengths to the light and dark bands.

At least you changed your link reference; but you still fail to see the blunt, obvious truth. Look at this picture:


Do you see that lines #1, 2, and 4 all go to different, arbitrary points along the width of the slit? The slit (already) MUST have a certain ratio to the wavelength of light passing through, and NOW, with the addition of "points" to measure from the slit to the screen, WHOLE FRACTION RATIOS are introduced into the equation, WITHOUT explanation. For now, just keep it simple, and ADMIT that you can see the red dots that are ADDED to the experiment (there are NO real barriers there) between the sides of the slit.



You have to ask yourself some questions like:

"WHY on Earth does line #4 go from the center of the slit, to the far left (to meet #3, which started from one side)??"
"WHY do lines 1 and 2 move in opposite directions??"
"WHY do lines 1 and 3 start from the same point, and move in opposite directions??"

There is a world of difference in "mapping out" what is happening, versus Physics.


regards,

T.Roc



This post has been edited by TRoc on Jan 16 2007, 07:16 PM

Deflection and refraction have also some based claim as to what angle the refraction or deflection takes place in.
Remember angles are like the bread to lights butter and must abide by specific rules when being defracted.

Even though light is spaced to spew forth at chaotic degree's and angles not alot of particles can attain they still must be deflected off something whether it be a lengthy distance or a shortened one.
They also need to be specific in how they refract, some light may catch itself being bounced off at another angle or be absorbed into a spectrum of light akin to its own particle make-up.

This post has been edited by ChaosTheory on Jan 16 2007, 07:24 PM

LL,


Just trying to address your question as to atomic transitions, electron orbitals, etc.

You can see my last post to C2 (above), what I call the "see-saw" equation approach to Science that is used to replace "understanding". Measuring what happens at the measurement, and then inferring an ad hoc "cause" at the "source".

It can be logical, but not always 100% true.

Drawing lines from a dark band in the diffraction pattern to "the middle" of the slit, and then deeming the middle of the slit as "negative", or causing destructive interference does not speak of the cause, it speaks to the effect.

The reason I say that now, is that just saying that "adding at least as much weight to 1 side of the see-saw will cause the other side to come down" doesn't explain WHY. (the Physics)

So, your statement:

is true to the extent that the Fraunhofer method is "true" for the DSE.

You must clearly define your "a photon": the emission photon will have exactly the same amount of energy (frequency) as the photon that was absorbed, by the orbital of the electron.

That statement is a process.

The discreet "jump" in energy is described as instantaneous, and the subsequent emission of the photon, as spontaneous relaxation, in a finite amount of time (yet to be accurately measured/predicted). These terms could be different, of course, but that's the basics.

If you are asking "does the orbital radius increase by the wavelength of the photon, in terms of distance", I think the answer is no.

The current method takes the "bound" energy of the atom, -13.6 eV for the H atom, and then, with every jump in energy, the electron becomes more loosely bound, until it is ionized, and "free".

We talked a little about the "frequency" of the crystal, or glass (transparent) being resonant with visible light (other specific frequencies). That is simple matter frequency resonance with energy frequency. Both parameters are able to change, and either would affect the results.

In a perfect world, with perfect black-bodies, perfect circles, etc., we could use Hydrogen to measure Hydrogen, and get ABSOLUTELY ACCURATE results.

However, in our world, we end up measuring things like Copper with Silicon, or whatever you can imagine. Everything that is not "identically" resonant, is what I term, a beat-frequency, which is always described as the difference between energy levels.

So, when Schroedinger attempted to set out to explain the quantum world with his "beat frequency" method, he was "swatted down" by "Boltzmann's Last Stand. Things were not going to be so "tidy".

However, I feel that they were actually looking at the "effects" only, and not the "cause". This was Einsteins complaint of Bohr's' "don't ask" response to questions of "why"; Bohr insisted that we ONLY look at the things that we can MEASURE. We can NOT "measure" what is happenING, only what has hapenNED. This is the motivation for Dirac's desire to keep photons interfering only "with themselves", so as to not have to "explain" any "new" parameters, that only exist "between" cause and effect. He still had his "sea of virtual photons" to "fill in the middle", so I don't think his answer is any better.

When you look at the "foundational" methods of Maxwell, you MUST include the "fields" as an "in between" parameter. Yes, I think fields should be included, and maybe even amended to include the "frequency cascade" that seems to be indicated in so many places. These are "wavelets", beat-frequencies, heat, "virtual particles", etc. (anything but the "real" photon)

A black and white world must include grey.

Positive/Negative/Neutral

The binary is built into the duality, but does not encompass it. The "third party" allows for the equilibrium state, as well as positive and negative, and "nothing".

I think that there is more to gleen at this point, from looking at theoretical causes, than from the "explanations" of the affects.


My "sidetrack" aside, did I answer your question?



ciao,

T.Roc



This post has been edited by TRoc on Jan 16 2007, 08:31 PM

Hi TRoc,ChaosTheory,
CT .. I think I preferred your schnozzle theory.
TRoc, at least least you continue to be 'evidence based'
For the present I can't find any better explanation of diffraction than hyperphysics .. clearly not good enough.
Here's a justification of the little sources
http://socrates.berkeley.edu/~phy7c/huygens.html
Back to diffraction..
A fairly 'proper' integration job is done here
http://en.wikipedia.org/wiki/Diffraction where the source is assumed to be infinitely narrow and calculus is used to get the answer.. I'm not sure this will help that much.
As a plausibility argument .. imagine a slit with a plane wave arriving on one side and the slit is 2 wavelengths wide.
If we imagine dividing the slit in two we can see that half the energy comes from one side and half the energy from the other. If we look at this from the point of view of a screen on the non-excited side we can (hopefully) see that there will be points where the one side is (on average) half a wavelength further away than the other .. so waves arriving from one side of the slit will be cancelled out by the waves from the other. For fun let's both try to work out what that angle is .. and see if we get he same answer.
Best wishes,
-C2.