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My plot is coming up empty. Can someone help me figure out why?

Posted 9 years ago
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Hi. I'm trying to get a plot, but although I think I'm doing everything correctly, the final plot comes up empty.

The code I'm using is below. Can someone tell me what I'm doing wrong?

p.s. Sorry about how the code looks. Copying the text from Mathematica seems to put it in this form.


Subscript[n, i] = 1.0;
\[Delta] = (4*\[Pi])/\[Lambda]*n*d*Cos[Subscript[\[Theta], 3] Degree];
Subscript[\[Theta], i] = 
  ArcSin[n/Subscript[n, i]*Sin[Subscript[\[Theta], 3] Degree]];
Subscript[r, s] = (
  Subscript[n, i]*Cos[Subscript[\[Theta], i] Degree] - 
   n*Cos[Subscript[\[Theta], 3] Degree])/(
  Subscript[n, i]*Cos[Subscript[\[Theta], i] Degree] + 
   n*Cos[Subscript[\[Theta], 3] Degree]);
Subscript[r, p] = (
  n*Cos[Subscript[\[Theta], i] Degree] - 
   Subscript[n, i]*Cos[Subscript[\[Theta], 3] Degree])/(
  Subscript[n, i]*Cos[Subscript[\[Theta], i] Degree] + 
   n*Cos[Subscript[\[Theta], 3] Degree]);
Subscript[T, s] = (1 - Subscript[r, s])^2/1;
Subscript[R, s] = (4*Subscript[r, s] Sin[\[Delta]/2]^2)/1;
Subscript[T, p] = (1 - Subscript[r, p])^2/1;
Subscript[R, p] = (4*Subscript[r, p] Sin[(\[Delta]/2) Degree]^2)/1;
Manipulate[
 Plot[{Subscript[T, s], Subscript[R, s]}, {Subscript[\[Theta], 
   3], -1, 1}, Frame -> True, 
  PlotStyle -> {{Thickness[0.004], 
     RGBColor[0, 0, 1]}, {Thickness[0.004], RGBColor[1, 0, 0]}}, 
  PlotRange -> {{-1, 1}, {0, 1}}, 
  PlotLegends -> {"T", "R"}], {{\[Lambda], 500*10^-9, 
   "wavelength \[Lambda]"}, 350*10^-9, 
  750*10^-9}, {{d, 5*10^-6, 
   "thickness d"}, (2*10^-6), (10*10^-6)}, {{n, 1.5, 
   "refractive index n"}, 1.33, 1.8}]

POSTED BY: Charles Stanley
8 Replies

However, I don't understand your comment about the difference with the Degree statement, because Rp and Rs seem to be identical in how the Degree statements are placed.

Snipped from the original post

degree

in the previous appendix comm3977321.nb the missing (?) Degree was put into Rs in an attempt to get the pictures right ... but unfortunately with no success.

POSTED BY: Udo Krause

Thank you for pointing out the plot range. I missed it because the lines are outside of where they should be.

I checked the formulae, and as far as I can tell, they appear to be correct. However, I will try to get external confirmation.

However, I don't understand your comment about the difference with the Degree statement, because Rp and Rs seem to be identical in how the Degree statements are placed.

p.s. If I didn't state it before, thank you for trying to help me with this.

POSTED BY: Charles Stanley

It's the PlotRange! In my picture the blue line is above y = 1 and the red line is well below y = 0 and in your first picture it is again said

PlotRange -> {{-1,1} (* right *), {0,1} (* too narrow for the formulae given ! *)}. 

Then please check the formulae, Rp has a Degree in it, the structural equal Rs does not have a degree. Something - which I didn't found - still prevents one to reach a physical meaningful picture (like the second one from your post), as seen from separat plots of Ts and Rs.

Attachments:
POSTED BY: Udo Krause

Udo, I tried it your way. I ended up with the same result:

http://i.imgur.com/RGwrOES.png

However, even with the plot you pulled up, it shouldn't be that flat. My understanding is that this is what it's supposed to look like:

http://i.imgur.com/m1D37Ym.png

Regardless, I'm not even getting the flat lines. Is there an obvious mistake I'm making?

POSTED BY: Charles Stanley

You need to bring the variables inside Manipulate, forget about subscripted variables as function names, beauty trades off by no way the troubles coming in from it

Manipulate

one might ask why the red and blue line a horizontal straight? That's because the variation is very small

variation

POSTED BY: Udo Krause

I'm not sure I follow. Do you mean in the cases where the degree symbol comes before the ArcSin argument?

How can you tell that it's non-numeric? And how am I misusing it?

POSTED BY: Charles Stanley

No -- What I thought wasn't it. N[[Degree]] gives a numeric result.( It is the same as N[1 [Degree]]

I'll look at it more later.

POSTED BY: Marvin Ray Burns

I'm not sure but, by troubleshooting, I see the following:

Table[{Subscript[T, s], Subscript[R, s]}, {Subscript[\[Theta], 3], -1,
   1}]

enter image description here

Notice how Degrees is being used in a non-numeric fashion in some cosine operations.

POSTED BY: Marvin Ray Burns
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