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24-Ruby III

## One optic problem - one physic constant n

At which value n the optic focus of lens is a geometric focus too?

See please two pictures and two Prime 3.1 sheets in attach.

1 ACCEPTED SOLUTION

Accepted Solutions
24-Ruby III
(To:ValeryOchkov)
16 REPLIES 16
24-Ruby III
(To:ValeryOchkov)

Where is an error?

24-Ruby III
(To:ValeryOchkov)

I have the function but with y as one more argument.

How can I delete y? Substitute y=1?

21-Topaz II
(To:ValeryOchkov)

the function n (a, b, y) has a pole at y = 0. So you have to exclude the pole in order to draw a graph.

24-Ruby III
(To:-MFra-)

Yes - a pole! How can I show that n(a, y)=sqrt(2)?

24-Ruby III
(To:ValeryOchkov)

How cam I delete in n(a, b) function? One way - insert 1 on the place y?

24-Ruby V
(To:ValeryOchkov)

> How cam I delete in n(a, b) function? One way - insert 1 on the place y?

Yes, or in Prime you better use NaN which unfortunately is not valid in Mathcad 15's 3D plots

24-Ruby III
(To:Werner_E)

Thanks, Werner, I knw it.

But how we can show analytical not by plot that n(a)=sqrt(2)

24-Ruby V
(To:ValeryOchkov)

> Thanks, Werner, I knw it.

So why did yo ask how to get rid of the pole in the plot??

> But how we can show analytical not by plot that n(a)=sqrt(2)

Doesn't your plot show that it isn't exactly sqrt 2  ??

EDIT: Looks that what we see here are numerical round offs.

I was not able to make Mathcad do the symbolic simplifications with general varaibles but at least for specific values (as long as a=b>=0):

24-Ruby III
(To:ValeryOchkov)

24-Ruby V
(To:ValeryOchkov)

> > But how we can show analytical not by plot that ...

24-Ruby III
(To:Werner_E)

It is a question!!!

I am preparing an article "Second optical property of hyperbola".

Would you like be a coauthor?

https://cdn2.mti.edu.ru/cloudofscience/CoS_3/CoS_3_396.pdf

I have only pointed "Thanks, Werner,  for help!"

24-Ruby V
(To:ValeryOchkov)

No, I was just confused that you closed the thread even though no full symbolic solution to your question was found.

24-Ruby III
(To:Werner_E)
 Werner Exinger написал(а): Wasn't your question > > But how we can show analytical not by plot that ...

24-Ruby V
(To:ValeryOchkov)

???

I don't see the correlation to n(a,b)=epsilon(a,b) for y=1, which is what you wanted to show (or at least thats what I got the impression you wanted to show with your plot).

Maybe I am missing the point!?

24-Ruby III
(To:Werner_E)

It is a new solution

24-Ruby III
(To:ValeryOchkov)
 ValeryOchkov написал(а): Werner Exinger написал(а): Wasn't your question > > But how we can show analytical not by plot that ...

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