Wavelength Measurement

[Dalo]

Let us start first with Klaynos' explanation, that wavelength concerns the distance between two peaks of the same wave. I would very much like to understand that before I look any further.

[swansont]

2 hours ago, Dalo said:

We are apparently not communicating very well. I want to know how the wavelength is calculated. I have read the information in textbooks and watched the videos, and I still have questions. My first question was answered, but it created its own questions.

The difference in distances between two lines, from the diffraction grating to the screen, is used to calculate the wavelength. I find it strange because both lines come from the same wave, while the wavelength is the distance between two waves.

How is that possible?

different cycle, as the wave from one slit has to travel one extra wavelength compared to the other, to get constructive interference 

[Dalo]

4 minutes ago, swansont said:

different cycle, as the wave from one slit has to travel one extra wavelength compared to the other, to get constructive interference 

you sound like you are not following the discussion at all.

[John Cuthber]

6 minutes ago, Dalo said:

you sound like you are not following the discussion at all.

To me, it sounds like you are not following it.

[Dalo]

I am just waiting for Klaynos' explanation.

[Strange]

30 minutes ago, John Cuthber said:

Does that make sense now?

Actually, even I'm confused by the proliferation of lines and colours now! And I already understand how the interference pattern arises.

Does this, slightly simpler, diagram help:

The blue dotted lines show the places where the peaks of the waves (green and purple) from each slit coincide (constructive interference; therefore bright spot on the screen). In between those positions there will be less light, with a minimum where the peak from one side coincides with the ... ermmm... "anti-peak" from the other.

 

 

Edited November 26, 2017 by Strange
fix image

[John Cuthber]

1 minute ago, Strange said:

Actually, even I'm confused by the proliferation of lines and colours now! And I already understand how the interference pattern arises.

Well, if you understand how the pattern is formed and you can see how the angle of the outgoing beams is defined by the grating's spacing and the wavelength, then what's to explain?

The grating spacing is known (because we make them with known spacings). The angles can be measured by finding out how far the beams spread when they reach a screen at a known distance.

So we can calculate the wavelength.

[Strange]

1 minute ago, John Cuthber said:

Well, if you understand how the pattern is formed and you can see how the angle of the outgoing beams is defined by the grating's spacing and the wavelength, then what's to explain?

I think it is just getting confusing with too much detail on one diagram ...

[Dalo]

2 minutes ago, John Cuthber said:

So we can calculate the wavelength.

But what is the wavelength? Is it the distance between two waves, or the distance between two peaks/troughs of the same wave?

[Strange]

3 minutes ago, Dalo said:

But what is the wavelength? Is it the distance between two waves, or the distance between two peaks/troughs of the same wave?

It is the distance between two peaks of the same wave. The peaks are represented by the red, green and purple dotted lines in my diagram. So the wavelength (shown as λ) is the distance between two red (or green or purple) dotted lines.

[Dalo]

1 minute ago, Strange said:

It is the distance between two peaks of the same wave. The peaks are represented by the red, green and purple dotted lines in my diagram. So the wavelength (shown as λ) is the distance between two red (or green or purple) dotted lines.

I must admit that I have never encountered this explanation of wavelength before. Every textbook or video I have consulted/watched, used the water wave model, and my questions were based on that model.

This opens a new line of questioning. Since they all have the same color (wavelength), and therefore the same diffraction property, shouldn't they be parallel to each other?

Also, I find the image of wavelength as the distance between peaks of the same wave very intriguing. In particular, I wonder whether the frequency of a wave also has to be calculated the same way?

[Strange]

1 minute ago, Dalo said:

I must admit that I have never encountered this explanation of wavelength before. Every textbook or video I have consulted/watched, used the water wave model, and my questions were based on that model.

This is kind of a "plan view" of the wave; whereas the normal sine-wave diagram is looking at it "sideways". The dotted lines show where the peaks of the sine waves are. But note that the peaks would be moving forward; this is just a frozen snapshot in time.

3 minutes ago, Dalo said:

This opens a new line of questioning. Since they all have the same color (wavelength), and therefore the same diffraction property, shouldn't they be parallel to each other?

They are (effectively). The read lines are the parallel peaks (of a plane wave). The green dotted lines are all the same distance apart - they are the concentric circles of waves from the slit. (Ditto the purple lines).

4 minutes ago, Dalo said:

Also, I find the image of wavelength as the distance between peaks of the same wave very intriguing. In particular, I wonder whether the frequency of a wave also has to be calculated the same way?

Yes. The frequency is the time between each peak of the wave - so it is related to the wavelength and the speed of the wave. [latex]f = \frac v \lambda[/latex]

[Klaynos]

4 minutes ago, Dalo said:

I must admit that I have never encountered this explanation of wavelength before. Every textbook or video I have consulted/watched, used the water wave model, and my questions were based on that model.

This opens a new line of questioning. Since they all have the same color (wavelength), and therefore the same diffraction property, shouldn't they be parallel to each other?

Also, I find the image of wavelength as the distance between peaks of the same wave very intriguing. In particular, I wonder whether the frequency of a wave also has to be calculated the same way?

Water waves are used as people are familiar with them. That causes issues as the language people use about them is very loose. What is one water wave? What we see hitting a beach is complicated. A wave comprising a single amplitude peak in the time domain is not a single wavelength wave. 

Look at a single frequency continuous sound wave, that's a simpler case to start with. 

To add, each crest isn't a new wave. 

[John Cuthber]

Here's a picture of some waves (slightly lumpy because I can't draw). The distance between the red marks is the wavelength.

Since all light waves travel at the same speed, the time between each wave crest passing a given point is fixed for any given wavelength

and the number of peaks passing a given point in a second is also fixed.

 

[Dalo]

32 minutes ago, John Cuthber said:

Here's a picture of some waves (slightly lumpy because I can't draw). The distance between the red marks is the wavelength.

Since all light waves travel at the same speed, the time between each wave crest passing a given point is fixed for any given wavelength

and the number of peaks passing a given point in a second is also fixed.

 

I confess: I am really confused.

When I look at your drawing (mine are even worse!), each single wavy line could represent a single wave, followed by others.

At the same time, each wavy line could be considered as many waves following each other.

It just depends how you look at it. So, I will just opt for the first perspective, each line represents a wave with different peaks and troughs.

If such a line has to go through a diffraction grating, the different parts that got through will form one wave again. But since they are all diffracted at the same angle, why should they ever interfere? Maybe I am thinking too much in ray terms, as I imagine them going through the slits and being diffracted. I have no trouble understanding that because the different parts are not all at the same level, a trough may meet a peak, and vice versa. This is not difficult to understand.

It becomes more difficult when thinking in rays. Why should they ever meet?

 

 

Concerning the law of speed of light (c=frequency times wavelength), I also do not understand how it can be applicable to the model of wavelength as distance between two peaks/troughs of the same wave.

The wave is moving in one direction, the frequency, at least in the water wave model, also concerns the number of waves that pass a border within a certain period. But the wavelength is now measured in a transverse way relative to the frequency. Is it a legal mathematical operation to multiply wavelength by frequency in such a model?

Edited November 26, 2017 by Dalo

[Strange]

19 minutes ago, Dalo said:

But since they are all diffracted at the same angle, why should they ever interfere?

Because they go through two different slits. So you end up with two waves from two different sources (the two slits). At different distances from the two slits, these two waves will have a different phase relationship. At some places the two peaks will coincide and the total amplitude will be double. In other locations, a trough and a peak will coincide and the total amplitude will be zero.

If you work out where the peaks coincide (either by using math or drawing diagrams) you will find that it forms radial lines (blue on my diagram). And the points where they cancel also form radial lines (in between these).

Edited November 26, 2017 by Strange

[Dalo]

9 minutes ago, Strange said:

Because they go through two different slits. So you end up with two waves from two different sources (the two slits). At different distances from the two slits, these two waves will have a different phase relationship. At some places the two peaks will coincide and the total amplitude will be double. In other locations, a trough and a peak will coincide and the total amplitude will be zero.

If you work out where the peaks coincide (either by using math or drawing diagrams) you will find that it forms radial lines (blue on my diagram). And the points where they cancel also form radial lines (in between these).

The diagram is perfectly clear, and interference is also perfectly understandable within the wave model. The ray model is what I have difficulty understanding. Since they all should have the same diffracting angle, shouldn't all rays, from whatever slit, be parallel to each other?

edit: this is assuming that they start as parallel rays from the source. Which is usually what is assumed in textbooks.

Also, I do not understand how we can use frequency and wavelength in the same equation to calculate the speed of light, when they are transverse to each other.

Edited November 26, 2017 by Dalo

[John Cuthber]

If a line of soldiers marches past you each moving at 2 meters per second and each one separated by 1 metre do you see why you are passed by 2 soldiers per second?

 

[Strange]

4 minutes ago, Dalo said:

The ray model is what I have difficulty understanding. Since they all should have the same diffracting angle, shouldn't all rays, from whatever slit, be parallel to each other?

Rays would be sent in all directions from each slit. So, some of those will be parallel but most won't be. (Rays are at right angles to the wavefront so where you have waves going out as concentric circles, the rays will be radial lines.)

6 minutes ago, Dalo said:

Also, I do not understand how we can use frequency and wavelength in the same equation to calculate the speed of light, when they are transverse to each other.

Nt sure what you mean by transverse to one another. They are measuring different things. Wavelength is the distance between peaks. Frequency is the rate at which peaks pass some point. So they are obviously related to the speed of the wave.

[Dalo]

3 minutes ago, John Cuthber said:

If a line of soldiers marches past you each moving at 2 meters per second and each one separated by 1 metre do you see why you are passed by 2 soldiers per second?

 

no idea what you mean by that.

[Strange]

2 minutes ago, Dalo said:

no idea what you mean by that.

Wavelength is the distance between the soldiers (distance between peaks).

Speed (of light or whatever) is the speed the soldiers are marching.

Frequency is the rate at which soldiers pass you.

It is what is known as an "analogy".

Edited November 26, 2017 by Strange

[swansont]

1 hour ago, Dalo said:

you sound like you are not following the discussion at all.

Count the number of wave peaks from each slit in Strange's drawing, to where you have constructive interference. On the m=1 line, the number will differ by 1. 

Like I said.

[John Cuthber]

1 minute ago, Dalo said:

no idea what you mean by that.

 

I don't understand how this is difficult.

Can you imagine a line of people standing one behind the other?

Can you imagine them all setting off walking?

Can you imagine standing next to that line.

They would walk past you.

If there was a gap of 1 metre between them, and they were walking at 2 metres per second then, in each second, 2 of them would walk past you.

[swansont]

10 minutes ago, Dalo said:

The diagram is perfectly clear, and interference is also perfectly understandable within the wave model. The ray model is what I have difficulty understanding. Since they all should have the same diffracting angle, shouldn't all rays, from whatever slit, be parallel to each other?

No. Huygens principle. Any point source (like a slit) radiates a spherical wave front. 

[Dalo]

time out. Not everybody at the same time. I will answer soon.