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Parabola-Mirror - an error?

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Emerald III

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:

7-36-Optic-Parabola.png

Mirror-Parabola-Odesolve-Prime.png

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

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Accepted Solutions

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

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...

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

Thanks, but

Re: Parabola-Mirror - an error?

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

Re: Parabola-Mirror - an error?

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.

Re: Parabola-Mirror - an error?

Here we go.

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

Werner