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Dec 28, 2015
03:09 AM

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Dec 28, 2015
03:09 AM

Parabola-Mirror - an error?

Where is an error? Help please!

(One more same problem What is not correct in this optic problem?)

I know other simple solution this optic task (see please bellow), but I would like use this:

Simple solution - symbolic (by WolframAlpha.com site) and numeric (with nanotechnology help😞

Solved! Go to Solution.

ACCEPTED SOLUTION

Accepted Solutions

Dec 28, 2015
12:01 PM

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Dec 28, 2015
12:01 PM

Seems to work for negative values of x only.

Not sure and I had not tried (Prime is crashing all the time with your sheet) but maybe you run into the same problems with tan as I did in my solution above (y' gets infinte when x=0)

WE

25 REPLIES 25

Dec 28, 2015
06:41 AM

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Dec 28, 2015
06:41 AM

What do you mean by this equation

and where does it stem from?

And why do you think that the argument of y´ should be a length (x(alpha)) while the argument of y is an angle?

If you write y´ here it has in any case to be the derivative with respect to alpha.

WE

Dec 28, 2015
09:53 AM

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Dec 28, 2015
09:53 AM

Yes, Werner - not alpha but x - see please bellow

Dec 28, 2015
10:50 AM

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Dec 28, 2015
10:50 AM

You may be able to keep alpha as the independend variable, but you can't use y'(x(apha)).

What you mean is

which Mathcad can't unserstand and you will have to replace it by

If you do so, other errors occur, though.

But I see you already rewrote your equations to accommodate for x as the independent variable, anyway.

WE

Dec 28, 2015
10:57 AM

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Dec 28, 2015
10:57 AM

Thanks, but

Dec 28, 2015
11:00 AM

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Dec 28, 2015
11:00 AM

Yes, I told you that you will run into other errors so it seems it was only the first mistrake in a row of others.

WE

Dec 28, 2015
11:17 AM

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Dec 28, 2015
11:17 AM

From unnecessary ballast freed system but I don't understand what the error message would like to tell us!?

Looks like Mathcad does not like both derivaties to be in one equation.

Dec 28, 2015
11:56 AM

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Dec 28, 2015
11:56 AM

Here we go.

It was necessary to introduce a dummy function and to redefine tan(). Not convincing, but at least it works.

Werner

Dec 28, 2015
09:33 AM

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Dec 28, 2015
09:33 AM

I think you need to do it like the following Valery:

Note that the gradient is infinite at x = -F, which leads to difficulties for the integration routine. Hence the definition of the gradient function above.

Alan

Dec 28, 2015
09:52 AM

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Dec 28, 2015
09:52 AM

Thanks, Alan and Werner.

The Prime 3 sheet in attach is without an error but has a false tan not sin in the last equation.

I feel the error but...

Dec 28, 2015
12:01 PM

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Dec 28, 2015
12:01 PM

Seems to work for negative values of x only.

Not sure and I had not tried (Prime is crashing all the time with your sheet) but maybe you run into the same problems with tan as I did in my solution above (y' gets infinte when x=0)

WE

Dec 28, 2015
02:55 PM

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Dec 28, 2015
03:28 PM

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Dec 28, 2015
03:28 PM

Do you know a surface with this Law of reflection:

The sin of the incident ray angle is equal the cos of the reflected ray angle.

What form of a mirror is valid for this Low?

Dec 28, 2015
04:28 PM

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Dec 28, 2015
04:28 PM

Why are you trying this the hard way?

Numerically it is possible to solve this, but it can also be done symbolically:

Here is an animation

Note that the solution also works when F is negative, then the mirror is convex instead of concave.

Luc

Dec 28, 2015
07:31 PM

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Dec 28, 2015
07:31 PM

Those embedded videos don't work (as so often).

Better simply attach the original avi-file.

-> Better qualitiy, more convenient to watch and more reliable

Here is what I see:

Dec 29, 2015
01:20 AM

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Dec 29, 2015
01:20 AM

Werner Exinger написал(а):

Those embedded videos don't work (as so often).

We must load not avi but mov files. I do so and no problem!

And it is good to attach avi and mov files to the messege.

Dec 29, 2015
06:06 AM

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Dec 29, 2015
06:06 AM

It should work with avi's, too. Having to convert animations to another format is an annoying additional step of operation.

But then, I never liked the embedded videos here in this forum for various reasons. Since the last forum design change it seems to have become worse.

Anyway, I played around with your last version and stumbled upon a quite strange effect.

**** DELETED *******

The real reason for the peculiar effect was sitting about 40 cm in front of the screen 😉

Werner

Dec 29, 2015
08:07 AM

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Dec 29, 2015
08:07 AM

OK, here is really a strange effect.

Why does this small change of the end value has such a big impact on the overall shape of the solution??

I could understand if the algorithm goes havoc near x=0, but not at the start at x=-F.

Or is it working from x.end back to the start? Don't think so as it has to use the initial conditions for x=-F first, I guess.

Werner

Dec 30, 2015
01:53 AM

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Dec 30, 2015
01:53 AM

A lens not mirror - but two video - from avi and mov files

Dec 29, 2015
06:49 AM

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Dec 29, 2015
06:49 AM

Luc,

Your animation is not visible for the viewing. Please attach to the message the archive of this animation.

Dec 31, 2015
09:32 AM

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Dec 31, 2015
09:32 AM

VladimirN. написал(а):

Luc,

Your animation is not visible for the viewing. Please attach to the message the archive of this animation.

See please:

Dec 29, 2015
08:22 AM

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Dec 29, 2015
08:22 AM

I noticed it wasn't visible. I even got to see my animation attachment efforts as separate items in the topics list:

but with NO access allowed. When I try to select one, Iget:

Here's a zip file with the AVi's.

Enjoy!

Luc

Dec 31, 2015
06:20 AM

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Dec 31, 2015
06:20 AM

Dear Luc, did you do this analysis in Mathcad 11 or Mathcad 15? If in MC11 would this work in 15 seen the different symbolic engine? Happy New Year and thanks for the many very instructive worksheets over the last years.

Dec 31, 2015
08:11 AM

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Dec 31, 2015
08:11 AM

LucMeekes написал(а):

Numerically it is possible to solve this, but it can also be done symbolically:

Symbolically it is possible to solve this, but it can also be done numerically:

Dec 31, 2015
08:47 AM

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Dec 31, 2015
08:47 AM

LucMeekes написал(а):

Why are you trying this the hard way?

I would like to solve this problem!

Do you know material of this mirror surface?

Dec 30, 2015
01:48 AM

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Dec 30, 2015
01:48 AM

How can we use the try (on error - Mathcad 15) operator: