# The Double Slit Experiment and the amplitude of light

1. Aug 2, 2014

### CapsE

I just saw a video about the so called "Double Slit Experiment" () which showed that two lightbeams that are parrallel will manipulate each other just like waves in a pond would do.

The slits used in this experiment were very close together but you could see them with your eye so I guess they were a millimeter or the tentht of a millimeter apart.

My question is: How big is the amplitude of light meaning the distance from the negative to the positive peak in millimeter (or any other unit of length). If the two beams in the video could interact with each other my conclusion would be that it must be at least half the distance of the two slits but if that's the case then why do glass fibre cables work? They should be much to small to allow such a big amplitude.

PS: I'm not a native speaker so I hope I didn't make to many mistakes ;)

Last edited by a moderator: Sep 25, 2014
2. Aug 2, 2014

### Staff: Mentor

The wavelength of the visible light ranges from about 700 nm to 400 nm, where nm is a nanometer, one billionth of a meter. Note that wavelength is different than a wavefront. A wavefront is like one peak or trough in the water waves in the video. It's an area where the phase of the wave is the same. The wavelength is the distance between each successive peak or trough. For the water waves in the video, this would have been a few inches.

When the light goes through the slits, it diffracts and the wavefront spreads out from each slit, allowing light from both slits to interfere with each other and form a diffraction pattern on the back wall of the box even though the wavelength is so small.

3. Aug 2, 2014

### CapsE

Ahh okay so the slits have to be narrow enough to get effected by Heisenbergs uncertenty principle for this to work? And if so why does it form a pattern? To my understanding the spreading caused by the uncertenty should be absolutly random.

4. Aug 2, 2014

### Staff: Mentor

No, this has nothing to do with the HUP. It's exactly as the video explained it. When the light hits the back wall, some of it is constructively interfering and some of it is destructively interfering, leading to the pattern created. See the following links.

http://en.wikipedia.org/wiki/Diffraction
http://en.wikipedia.org/wiki/Interference_(wave_propagation [Broken])

Last edited by a moderator: May 6, 2017
5. Aug 2, 2014

### CapsE

I get that the waves influence each other but I don't get my mind around why. If the two beams go straight through the slits their amplitue (y) has to be somewhere in the dimension of the distance between the slits (x) so that an "impact" or distorcion could take place.

Or is it like I tried to show with the green line that the light changes direction while passing the slit?

This image should be more acurate but if it is I don't get why the two beams influence each other. (y again is the amplitude of the lightwave.)

6. Aug 2, 2014

### Staff: Mentor

That amplitude is not a distance at all. Those pictures that show wavy lines are graphs, with the strength of the electric field on the vertical axis and time on the horizontal axis. They show the strength of the field over time at a single point.

7. Aug 2, 2014

### Staff: Mentor

They can also be interpreted as showing a "snapshot" of the strength of the electric field versus position at a single instant (point in time), along a line in the direction that the wave is propagating.

To the OP: the linked post below leads to a better representation of what a snapshot-in-time of an electromagnetic wave "looks like" than the typical sine-wave graph than you see in textbooks and elsewhere. Follow the link in that post to see the diagram and some description of it. Then read the rest of the first thread for some discussion clarifying the diagram.

8. Aug 2, 2014

### CapsE

Okay I think I get it now. Thanks for the help :)

9. Aug 2, 2014

### olivermsun

I think the OP was asking whether the slits themselves have to be narrow enough that diffraction effects become important, in which case I would tend to say yes, this is closely related to the HUP.

10. Aug 2, 2014

### Staff: Mentor

And that is not correct, as the video linked in his first post shows by having slits large enough to see with the naked eye. The HUP has absolutely nothing to do with how the double slit experiment works.

11. Aug 2, 2014

### olivermsun

I'm confused. Isn't diffraction commonly visible through apertures that are large enough to see with the naked eye?

12. Aug 2, 2014

### Staff: Mentor

Yes, which is why the HUP has nothing to do with this. The HUP only matters at the atomic scale.

13. Aug 2, 2014

### olivermsun

What are you talking about? The slit is a space constraint. The diffraction pattern is related to the uncertainty in momentum of the photon.

14. Aug 2, 2014

### Staff: Mentor

I will find diffraction if I solve the classical wave equation for light as electromagnetic radiation impinging on a slit. The uncertainty principle is irrelevant.

15. Aug 2, 2014

### olivermsun

Do you think the uncertainty principle is irrelevant to underlying phenomenon, or just irrelevant to your particular method for calculating the pattern?

16. Aug 2, 2014

### Staff: Mentor

Pretty much completely irrelevant, especially for photons for which the position is undefined except when they're interacting with something. When we do a single-slit diffraction experiment with massive particles such as electrons which do have a position, the uncertainty in the electron's position when it hits the screen is small compared with the width of the diffraction fringes.

17. Aug 3, 2014

### olivermsun

The photon is interacting with the slit (and later the screen), which counts as something and therefore constrains the position, right?

Edit: Maybe I'm just not understanding what the disagreement is about, but the OP asked whether the slit needs to be narrow enough for HUP to come into play; and at least on a superficial level this appears to be a "yes" just judging from the respective equations for HUP and for diffraction through a slit.

Last edited: Aug 3, 2014
18. Aug 3, 2014

### Staff: Mentor

And I don't see how you're coming to that conclusion. The slits in the video aren't narrow at all compared to the wavelength of the light. Besides, the OP doesn't even understand how classical light waves work. There's no reason to even talk about quantum mechanical effects at this level of understanding. It's just confusing.

19. Aug 3, 2014

### davenn

Agreed

His ( the OP) first pic in post #5 is incorrectly interpreting the wavefront of the light source and therefore the interference pattern produced as shown in the video.
He needs to watch the video again and see the part where the waves were created in water and produced an interference pattern. Then realising that the same is happening with the sunlight through the slits in the cardboard box
Classical physics explains the phenomena without getting into QM and HUP

Dave

20. Aug 3, 2014

### olivermsun

Well, in the video they actually state that the slit is very narrow.

Also, if you look closely at the equation for [URL="http://en.wikipedia.org/wiki/Fraunhofer_diffraction#The_Fraunhofer_diffraction_equation]Fraunhofer diffraction[/URL], you'll notice that the necessary condition is not $W \ll \lambda$ where $W$ is the slit width and $\lambda$ the wavelength. It's actually $W^2 \ll \lambda L$, where L is the distance to the screen. Even for quite large apertures, the diffraction can be noticeable when $L \gg \lambda$.

The OP asked. (S)he should receive a correct answer, even if it comes with a disclaimer of "Not necessary for understanding this problem." In this case the answer is the same whether you appeal to classical wave theory or HUP: the slit needs to be narrow, but not invisibly narrow.