Wavelength Measurement

[Dalo]

Wavelength refers to the distance between two crests or between two troughs.
Imagine standing on the beach and looking at the waves coming towards you. 
The waves can cover a long distance along the beach, let us call it their width, but that is irrelevant. What you want to know is how often they follow each other (frequency), how high they get (amplitude), and of course what we have referred to as their wavelength.

Here is a genuine question:
To measure the wavelength, we are told to measure the distance between the points on a screen of (monochromatric) light that has come through two or more slits.
This is a horizontal distance, comparable to the width of the waves hitting the sand. But we want the distance between the crests or the troughs. Which is, seen from the perspective of someone standing on the beach, a vertical distance.
Imagine erecting a barrier somewhere in the water, with a diffraction grating, and measuring the points where the water comes through.
Apparently, you would be measuring points along the width of the wave, and not the distance between crests or troughs.
So, what is the real explanation when dealing with light?

Edited November 26, 2017 by Dalo

[John Cuthber]

Does this help clarify things?

https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/diffraction-grating

 

[Dalo]

16 minutes ago, John Cuthber said:

Does this help clarify things?

https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/diffraction-grating

 

I was going to post exactly the same link! You beat me to it by a few seconds.

My first reaction was: yes, it does make sense. It is not the horizontal distance (from the perspective of one standing on the beach) that is measured, but the difference in distance light has to travel from each slit to the screen.

But then another problem came up, and I hope that it will also be as easily solved. The distances measured concern one and the same wave. My question is, how does that relate to the distance between two crests/troughs?

 

Well, almost the same link:

 

Edited November 26, 2017 by Dalo

[John Cuthber]

If you choose light of a single colour, the wavelength of all the light is the same.

Do you understand how the angle between the diffracted rays depends on the wavelength?

http://www.cyberphysics.co.uk/topics/light/A_level/difraction.htm

[Dalo]

Just now, John Cuthber said:

If you choose light of a single colour, the wavelength of all the light is the same.

Do you understand how the angle between the diffracted rays depends on the wavelength?

http://www.cyberphysics.co.uk/topics/light/A_level/difraction.htm

But we are still in the process of calculating the wavelength, defined as the distance between two crests/troughs. Your link already presupposes the calculation?

[swansont]

3 hours ago, Dalo said:

Wavelength refers to the distance between two crests or between two troughs.
Imagine standing on the beach and looking at the waves coming towards you. 
The waves can cover a long distance along the beach, let us call it their width, but that is irrelevant. What you want to know is how often they follow each other (frequency), how high they get (amplitude), and of course what we have referred to as their wavelength.

Here is a genuine question:
To measure the wavelength, we are told to measure the distance between the points on a screen of (monochromatric) light that has come through two or more slits.
This is a horizontal distance, comparable to the width of the waves hitting the sand. But we want the distance between the crests or the troughs. Which is, seen from the perspective of someone standing on the beach, a vertical distance.
Imagine erecting a barrier somewhere in the water, with a diffraction grating, and measuring the points where the water comes through.
Apparently, you would be measuring points along the width of the wave, and not the distance between crests or troughs.
So, what is the real explanation when dealing with light?

There's a reason why we use more precise terms like amplitude, and wavelength, rather than horizontal or vertical distance. It helps reduce the confusion.

The distance between waves is not a vertical distance. Any perception of that is an illusion from perspective, which is precisely the kind of thing you try and eliminate by doing a rigorous measurement.

[Dalo]

1 minute ago, swansont said:

The distance between waves is not a vertical distance. Any perception of that is an illusion from perspective, which is precisely the kind of thing you try and eliminate by doing a rigorous measurement.

Please do.

[swansont]

5 minutes ago, Dalo said:

But we are still in the process of calculating the wavelength, defined as the distance between two crests/troughs. Your link already presupposes the calculation?

That's the definition of wavelength. It's a given in the problem. It "presupposes" nothing.

Just now, Dalo said:

Please do.

Please do what?

[Dalo]

3 minutes ago, swansont said:

That's the definition of wavelength. It's a given in the problem. It "presupposes" nothing.

Then I simply do not understand the argumentation. How can it be a given?

edit: I understand the definition being a given, but the question now is how it is calculated.

John! Are you there? We were doing so well, and then you left me, and then this Terderator came out of nowhere and I think he is mad as hell!

Edited November 26, 2017 by Dalo

[swansont]

8 minutes ago, Dalo said:

Then I simply do not understand the argumentation. How can it be a given?

edit: I understand the definition being a given, but the question now is how it is calculated.

John! Are you there? We were doing so well, and then you left me, and then this Terderator came out of nowhere and I think he is mad as hell!

You can derive the interference pattern based on the wavelength. You can measure the interference, and solve the equation for the wavelength.

[Dalo]

1 minute ago, swansont said:

You can derive the interference pattern based on the wavelength. You can measure the interference, and solve the equation for the wavelength.

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?

[John Cuthber]

16 minutes ago, Dalo said:

this Terderator came out of nowhere and I think he is mad as hell!

That's further  use of the  wrong language.

You should try to avoid it.

 

[Dalo]

Just now, John Cuthber said:

That's further  use of the  wrong language.

You should try to avoid it.

 

there is something as humor. Banishing it would be very sad. But I will auto-censure. 

[John Cuthber]

OK, I have a mercury lamp.

It emits light of a number of different colours.

If I let the light shine through a piece of green glass then only the green light gets through.

If I pass it through a prism it doesn't split into different wavelengths - it's pretty nearly monochromatic.

How do I go about measuring the wavelength?

 

There are a couple of options reasonably easily available

 

It's a lot easier to work with beams of light if hey are nice parallel  beams. So I will start by passing the green light through a pinhole.

Then I can use a lens for make the light into a parallel beam.

Does that make sense so far?

 

 

[Dalo]

Let me see if I get it right:

Green light, when measured the way described above, gives a certain figure. And so does each other color, each color having its own figure. And, that is what we call wavelength.

If that is the case, then the mode of calculation does not fit the definition. You cannot define wavelength as the distance between two (monochromatic) waves, and then use another property of waves to calculate it.

Because of diffraction, the distances from the grating to the screen are particular to each color, but that has nothing to do with the original definition.

At least, I find it very difficult to link them together.

The calculations are legitimate and give us a very useful way of identifying colors, but they do not seem to follow from the definition.

 

Edited November 26, 2017 by Dalo

[John Cuthber]

46 minutes ago, Dalo said:

At least, I find it very difficult to link them together.

Nevertheless, they are linked.

Are you aware of this way to measure the wavelength?

http://www.schoolphysics.co.uk/age16-19/Wave properties/Interference/text/Wedge_fringes/index.html

[Dalo]

5 minutes ago, John Cuthber said:

Nevertheless, they are linked.

 

could you please elaborate?

As far as the fringes are concerned, I am not doubting the validity of the methods for measuring the distance between them

[John Cuthber]

OK, here's the picture from the site I cited earlier.

 

The picture is a plan view of light coming in from the left, hitting the grating and then spreading out from the holes in that grating as a series of circles (in green)

The green circles represent the peaks of the waves as they spread out. The distance between the circles is the wavelength of the light. The centres of the circles are the gaps in the grating. 

In reality the grating have thousands of lines and they are separated by something like a thousandth of a millimetre.

Does that make sense so far?

 

[Dalo]

Yes, but it is entirely irrelevant to the question: how does the distance between the fringes relate to the distance between the waves, assuming that all the waves hitting the screen at the same time originate from one and the same wave front going through the slits?

(it would be even more complicated if they did not)

Your diagram would be valid even if we changed the distance between two crests or troughs. The results would be the same, or so it seems to me.

Edited November 26, 2017 by Dalo

[John Cuthber]

It is relevant.

You can see the blue lines on the right of the diagram which show where the green circles line up- they go through all the points where the peaks in the waves are (because they go through the points where the green circles overlap).

The angle of those lines to the vertical depends on the size of the circles (the wavelength) and on the distance between their centres (the grating spacing).

Do you see that?

 

[Dalo]

I see the drawing and it explains what you say. But it does not explain the link between the distance between the fringes and the distance between the waves prior to passing through the grating.

You have no way of measuring the distance between the peaks and the troughs on the right side. All you have is the distance between the grating and the screen.

The way the calculations are made may explain the effect of diffraction on the distance traveled by light to the screen, but it does not explain the distance between two waves.

Edited November 26, 2017 by Dalo

[John Cuthber]

The wavelength doesn't change when it goes through the grating.

So the radii of the circles differ by exactly one wavelength.

The light carries on following a line perpendicular to the blue lines  i.e. in the direction of the red lines on the RHS of the diagram.

After a while, they hit the screen.

 

 

[Klaynos]

1 hour 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?

The wavelength is the distance between two peaks of the same wave. Not two different waves.

This is confused by water waves which are complex, and confused by language where every peak is often called an individual wave. 

[Dalo]

 

2 minutes ago, Klaynos said:

The wavelength is the distance between two peaks of the same wave. Not two different waves.

This is the first time I have ever heard of that.

4 minutes ago, John Cuthber said:

So the radii of the circles differ by exactly one wavelength.

Not by these calculations.

Edited November 26, 2017 by Dalo

[John Cuthber]

Hopefully Klaynos' explanation has helped.

If there wasn't a series of peaks with the waves at fixed intervals there couldn't be a "wave length"

 

OK, the waves travel on to the screen + form a dot of light there

You might have realise that there are other lines (like the blue ones) that you can draw through the intersections of the circles.Here's a rough sketch.

The purple lines represent the wave fronts of the beam of light that goes straight through the grating.

The yellow lines represent those which are "bent" even more by the grating. And obviously, there are similar lines for light bent towards the top of the diagram.

So the diffraction pattern is a series of spots centred on the "straight through" line.

Does that make sense now?