One optic problem - one physic constant n

[ValeryOchkov]

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.

[ValeryOchkov]

Where is an error?

[ValeryOchkov]

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

How can I delete y? Substitute y=1?

[-MFra-]

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.

[ValeryOchkov]

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

[ValeryOchkov]

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

[Werner_E]

> 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

[ValeryOchkov]

Thanks, Werner, I knw it.

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

[Werner_E]

> 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):

[ValeryOchkov · Accepted solution]

[Werner_E]

Wasn't your question

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

[ValeryOchkov]

It is a question!!!

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

Would you like be a coauthor?

In this article

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

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

[Werner_E]

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

[ValeryOchkov]

Werner Exinger написал(а):

Wasn't your question

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

[Werner_E]

???

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!?

[ValeryOchkov]

It is a new solution

[ValeryOchkov]

ValeryOchkov написал(а):

Werner Exinger написал(а):

Wasn't your question

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