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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
December 28, 2015
Solved

Parabola-Mirror - an error?

  • December 28, 2015
  • 4 replies
  • 12193 views

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:

7-36-Optic-Parabola.png

Mirror-Parabola-Odesolve-Prime.png

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

Best answer by Werner_E

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

4 replies

W
Werner_E25-Diamond I
25-Diamond I
December 28, 2015

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

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
December 28, 2015

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

W
Werner_E25-Diamond I
25-Diamond I
December 28, 2015

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

A
AlanStevens19-Tanzanite
19-Tanzanite
December 28, 2015

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

g0.PNG

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

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
December 28, 2015

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...

W
Werner_E25-Diamond IAnswer
25-Diamond I
December 28, 2015

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

L
LucMeekes23-Emerald IV
23-Emerald IV
December 28, 2015

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

Video Link : 6592

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

Video Link : 6593

Luc

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Werner_E25-Diamond I
25-Diamond I
December 29, 2015

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:

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
December 29, 2015

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.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
December 30, 2015

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

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