Diffraction

[TheRajinator]

I don't understand how in a single slit experiment with only one light source, the diffraction of light can cause a pattern of nodals and anti-nodals. There is only one wave of light hence how can it interfere and cancel out to form the patterns. Any explanation would be appreciated.

[Lasercookie]

It's important to not treat a wave like a particle. Just because there's 'one wave of light' doesn't mean that it's going to land straight on the screen like a particle would.

So having said that, how does a wave propagate then? I think it's pretty important to get this pretty clear in your head.

This is mentioned in the textbook somewhere, but there was Huygen who proposed the wave model for light. He had this idea where we consider each point on a wave of light to be a "point source" (in other words, a starting point) for smaller wavelets of light to be produced. If I'm not mistaken, this idea is referred to as Huygen's Principle.

So with single slit diffraction, we have a wave of light, which produces many smaller wavelets of light and it is these wavelets that interfere with each other and hence why we get our pattern.

This webpage might help: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html#c1

[TheRajinator]

Hmmm...I am still a bit confused... so essentially the light wave produces it's own smaller waves which cancel each other out hence causing a pattern. This seems new to me never heard of it, how does one wave become smaller waves. If we did this with water riples for example and had a sinlge slit, would there really be an interference pattern on the wall, meaning will there really be water waves that produce smaller waves that cancel out? The lines on the1st diagram from your link, how do the lines meeting at one point show constructive or destructive interference.  Lol I don't know if i'm just confused or the topic is confusing...

[Lasercookie]

iaodjidjidj I accidentally clicked close tab and then said pressed refresh after I got that confirm form resubmission prompt (i'm an idiot -_-) and lost the hours worth of work that I put into writing a response (you can probably tell I really liked this area of study ) -___________________- (lesson learnt: write AN posts in word or something with an autosaving feature first)

I don't really have the motivation to start writing from scratch again, but I feel bad about leaving you hanging without a response, so here's a rough summary of what I had written (I don't think it'll be as coherent without as much explanation though). I'll give you a lot of links / textbook references instead. I'm assuming you have Heinemann Physics.

1. Yes it is confusing.

2. So you're probably thinking of light moving something like this, being composed of individual 'wavefronts' that move their way forward.

It's natural to think then that "why would they interfere, they're moving separately?"

3. But I think a better question to ask is "how do they move in the first place?" Don't forget that these are waves we're talking about. You know that waves exhibit a "net transfer of energy, without a net displacement of matter". How could the waves themselves be travelling along?

Think of a sound wave. The particles vibrate, but they don't physically move from their position. A light wave is similar. It moves forward by producing smaller waves, and then these waves produce another set of waves and the cycle continues.

4. How does it do this? What is the medium here? Now recall that light is an electromagnetic wave. What is an electromagnetic wave, what does it look like? Something like this: http://en.wikipedia.org/wiki/File:Onde_electromagnetique.svg

It has an electric field component, and a magnetic field component. Page 417 of Heinemann probably gives a good enough explanation of how electromagnetic waves can be self-propagating (that last term is probably the key here).

5. So what are these wave fronts then? Page 407 Heinemann

Keep going back to this picture. http://upload.wikimedia.org/wikipedia/commons/6/60/Refraction_on_an_aperture_-_Huygens-Fresnel_principle.svg

You can picture it starting from the point source, and then new waves being produced. This is essentially Huygens principle. This is the fancy wording:

"every point to which a luminous disturbance reaches becomes a source of a spherical wave; the sum of these secondary waves determines the form of the wave at any subsequent time" and also sometimes stated that:

"Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets."

That probably makes no sense without pictures. Pictures are good stuff.

http://library.thinkquest.org/27356/p_huygens.htm
http://farside.ph.utexas.edu/teaching/316/lectures/node150.html

If you look at the various pictures of these wavelets, you'll probably be able to see how the wavefronts are formed. If you take a look at the point source, and then imagine a wave produced there, and then that's another point source for another wave and so on, and then draw out the wavefronts, you'll be able to see how the wave fronts appear to move along.

6. What is in phase and out of phase ? What does this have to do with interference? Principle of superposition blahblahblah
The mechanism section here: http://en.wikipedia.org/wiki/Interference_(wave_propagation)#Mechanism

6a. Tangent: You can model a wave as a sine wave. If you have a product function of two sine waves, what  does their resultant look like? What happens if you apply horizontal translations to one of those. Try 180 degrees, 90 degrees, 0 degrees etc. and see what the resultant wave looks like. How does this link to intensity (relates to 8a too)

7. You should be able to draw many parallels to double slit. In fact, it's probably easier to see with double slit why these wavelets would interfere with each other: http://www.pa.msu.edu/courses/2000fall/PHY232/lectures/interference/twoslit.gif

Again you can also see the wavefronts / smaller waves being produced. You can also see where they align / don't align and hence constructive and destructive interference.

8. Compare the intensity patterns you get for single slit and double slit. Why does this occur?

The plots I'm talking about are at the bottom of page 413 for double slit, and in the bottom right of page 415 for single slit.

8a. This was a bit of a tangent. Continuing on from part 6, you can see that you're not going to get little sets of straight lines, but rather a smooth curve, why? Because the waves will be out of phase, but they won't be perfectly out of phase as they are with destructive interference. Nor will they be perfectly in phase, such as you get with constructive interference. This means that you'll get some level of intensity. As you decrease/increase angle, you'll have the intensity slowly taper off.

8b. Continuing on from part 7, you can see if you look at the difference in the wavelets produced. (again we're looking at the pictures) With double slit, they're perfectly in line really. With the single slit, as you move to the left of the slit, and to the right of the slit, it seems to become a mess to follow.

i.e. in this picture (single slit) http://upload.wikimedia.org/wikipedia/commons/6/60/Refraction_on_an_aperture_-_Huygens-Fresnel_principle.svg

9. Yes you can consider water waves to produce wavelets as per Huygen's principle. http://www.youtube.com/watch?v=egRFqSKFmWQ It's hard to pick out, but there is maximums and minimums there.

Sorry, this post is a bit of a mess and I was a bit lazy with retyping it, but it gives you a starting point for reading/googling.

[TheRajinator]

Thanks man, really appreciate the detailed answer, I understand now, thanks