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 Author Topic: Fermat's principle  (Read 23463 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: July 13, 2012, 08:01:42 pm » posted from:,,Satellite Provider

In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time.

The following simulation let students play with Fermat's principle.

The ideas come from Vim Peeters:

a student should be able to choose a certain path of light between two points (which he can also use) in different optical media.

The applet would calculate the time the light needs to go from one point to another.

There are two slider on the left which can be used to adjust refraction index for both media (top/lower half).
User can drag red dot to change different path. The time for each path will be shown in the lower half panel.
Blue dot and Green dot can be drag if the drag check box is checked.

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wim peeters
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 « Embed this message Reply #1 on: July 14, 2012, 02:31:55 am » posted from:Hooglede,West-Vlaanderen,Belgium

hello
thank you for this effort. If possible, I would like the following changs to be made:
1. Simply indicate the speed of light of both media on the left, instead of the complicated formula n1/sin...: the sliders should vary, let us say between 50 million m/s and 299 792 758 m/s (by definition the max in vacuum!!!)- it would be nice that this number appears as maximum.
In this way both directions can be simulated.

2. Is it possible to drag the two points to other places as well??

3. Other question: do you know of a tool that can be superimposed on the computerscreen and that acts as an meter of the angle between two lines? I would need it to determine angles of forces that act given photo's or certain daily live situations. It should be possible to make it pop up, drag it to a certain place on the screen, and to point one leg in one direction, the other in another direction, and the angle between both legs appears. You understand that I could also use this in the optics simulation (later, after the sine function is known)

Thank you very much!
I hope you had a good time in Troya hotel, with all the water melon!

Wim  (PS Not Vim :-)  )
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wim peeters
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 « Embed this message Reply #2 on: July 14, 2012, 02:40:09 am » posted from:Hooglede,West-Vlaanderen,Belgium

Sorry, Fu Kwun, delete the last remark on dragging the two points: I found the click box to deal with that  :-)
Wim
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Fu-Kwun Hwang
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 « Embed this message Reply #3 on: July 14, 2012, 08:05:22 pm » posted from:,,Satellite Provider

Dear Wim:

I add some display on the right, so it will show speed of light at both media.
The slider still change the index of refraction, however, the speed will be displayed.

The above simulation has been updated with new version. I hope this is closer to what you want.
Let me know if you need more improvement.

Yes. I do enjoy the water melon while I was in Istanbul. :-)
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wim peeters
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 « Embed this message Reply #4 on: July 16, 2012, 06:03:07 pm » posted from:Hooglede,West-Vlaanderen,Belgium

Dear Fu-Kwun
Giving the two speeds is a lot better indeed. In this way it is obvious where it is all about.
The strange thing is that both with the sliders and the lower graph the axis is pointed downward, giving higher values when going down.
We are used to axis pointing upward, giving higher values when higher up. Is it possible to change that?

Another improvement would be to add the SUM of t1 and t2, to make it very clear also graphically where the real minimum is.

(Since you invite me to launch more ideas….)

Thirdly, new idea, is to take identically the same applet, but to change v so that it changes between 0,5 and 10 m/s for both “media” and the corresponding time is then in seconds, not ns. Why? This would correspond to situations like water/beach, water/riverbank, grass/asphalt, deep sand/ grass etc. . I am thinking of an active teaching method that goes as follows: there is a line on the playground, and on each side there is a mark, 10-20 m away from the line. Learners should go from one mark to the other, in one “medium” walking, in the other running, or in one walking, in the other on their knees. Or running, and hands and feet-running. To create two different speeds in any case. Which path to take? The simulation would make it clear one more time that it is not the shortest, but the fastest way that is valid.

In my previous mail, about the rounded edge: see attachment for a quick drawing: inside the rounded area there is water, outside is air (in principle). An object of dimensions AA’ looks thicker (see dotted lines) when looking from outside. I would just take a dot A and B to drag around, and the light goes via the round border from A to B. The point on the border follows the rounded curve now. The calculations are the same basically I guess.

Fu-Kwun: The sum of t1+t2 was already shown in the lower plotingPanel.
The higher the green curve , the lower the sum of t1+t2.

Wim: Sorry, I did not understand it, because in my view the graph was upside down: I did not recognise the minimum where it was in your graph a "top" of the curve.
So the only thing that is really is still  needed before I can "sell" it to my teachers is putting the plot upside down (max above, minima below).
Thank you again.
Wim

 « Last Edit: July 16, 2012, 06:07:39 pm by wim peeters » Logged
Fu-Kwun Hwang
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 « Embed this message Reply #5 on: July 16, 2012, 07:59:59 pm » posted from:,,Satellite Provider

Dear Wim:

The applet has been modified again. Two slider were added a the right hand side to adjust the velocity.
The time trace as function of space were re-draw from the bottom, now students can find minimum of t1+t2 from the curve. (It was maximum).

About the third option: change speed to 0.5-10 m/s. Would you like it to be another simulation, or I can add another option so the scale can be changed. Let me know which way you prefer.
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wim peeters
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 « Embed this message Reply #6 on: July 17, 2012, 01:25:46 am » posted from:Hooglede,West-Vlaanderen,Belgium

Dear Fu-Kwun
it is better to make it a separate EJS: in a learning line this one would come first, refelcting daily "logic" in "saving a person's life" or "winning a contest", apart from a logic that takes every driver from A to B in the least time.
Then I would use the refraction as a study that follows this logic: also nature acts within 'the least time" logic. This makes sense then to 13-14 years old learners. Refraction becomes aan application of what happens in daily life, with an in dept understanding of nature.
Snellius' law does not offer that conceptual understanding.

Too many variables in one applet confuses and makes it difficult for the teacher to focus on what needs to be learnt by the students.

Thank you again, we are moving quickly!!!

Wim
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Fu-Kwun Hwang
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 « Embed this message Reply #7 on: July 17, 2012, 04:03:11 pm » posted from:,,Satellite Provider

How about the following one! Let me know what need to be changed!

It is my habit to create simulation for teaching and learning. Let me know whatever you have in mind and I will try to find free time to do it.
:-)

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!
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lookang
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http://weelookang.blogspot.com

 « Embed this message Reply #8 on: December 22, 2015, 03:01:20 pm » posted from:SINGAPORE,SINGAPORE,SINGAPORE

i have re create a #JavaScript version here
http://iwant2study.org/ospsg/index.php/interactive-resources/physics/04-waves/04-light/114-fermat-princple-model-refraction-example
Enjoy!
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Progress is impossible without change; and those who cannot change their minds cannot change anything. ..."George Bernard Shaw(1865-1950, Irish dramatist, essayist and critic, Nobel Prize for Literature 1925)"