I'm quite new to Mathematica language, I am trying to figure out where I am making mistakes in Plotting a specific function that depends to other variables:

I want to plot

   Manipulate[Plot[{Im[fxDBL[φW, Λg]], 
   Im[fyDBL[φW, Λg]]}, {φW, 19, 
   23}], {Λg, 1.800, 2.500}]

I am defining the function fxDBL as

solution = Solve[φrad == π/2 + 1/2 (-π + aa - bb) + bb, aa];

fun = TrigExpand[Λg*λ/nres == Sin[aa - φrad] + Sin[bb + φrad]] /. solution[[1]] // Simplify;

solution2 = bb /. Solve[fun, bb] /. C[1] -> 1;

fxDBL[φW_,Λg_]:= ArcSin[nres*Sin[φW*π/180 - solution2[[2]]]]*180/π /. φrad -> φW* π/180;

but nothing is displayed... even if.., if I copy the final numerical output and defining fxDBL as

fxDBL[φW_, Λg_] := (
  180 ArcSin[
    1.49` Sin[(π φW)/180 - 
       ArcCos[0.17852348993288591` Λg Csc[(π \

Mathematica plots correctly the function I need.

what am I missing? is it something related to the output of Solve that is not used properly with solution2[[2]]? Thank you

  • $\begingroup$ In your code here, λ and nres are not defined, but I assume they are equal to 0.532 and 1.49? $\endgroup$
    – Jason B.
    Commented Feb 22, 2016 at 10:15
  • $\begingroup$ How is fyDBL[φW, Λg] in Manipulate defined? The code doesn't work even if you delete it, but the definition is missing $\endgroup$
    – mattiav27
    Commented Feb 22, 2016 at 10:18

1 Answer 1


The problem is that when you make the substitution /. φrad -> φW* π/180, the term φrad doesn't appear in the expression to the left. You can solve this in two ways, either use Set instead of SetDelayed,

fxDBL[φW_, Λg_] = 
     nres*Sin[φW*π/180 - 
        solution2[[2]]]]*180/π /. φrad -> φW* π/180

or use Evaluate,

fxDBL[φW_, Λg_] := 
     nres*Sin[φW*π/180 - 
        solution2[[2]]]]*180/π /. φrad -> φW* π/180]

Now your Manipulate works fine (assuming you define fyDBL at some point as well)

enter image description here


If you want to export your Manipulate as a gif animation, the non-intuitive way to do it is to export first as a movie, import that movie and export as a gif.

ManToGif[man_, name_String, step_Integer: 1] := 
  moviename = 
   name <> If[$OperatingSystem === "MacOSX", ".mov", ".avi"];
  Export[name <> ".gif", 
   Import[Export[moviename, man], "ImageList"][[1 ;; -1 ;; step]]];

This was adapted from Vitaliy's post on the community

  • $\begingroup$ May I ask how you made the movie of the manipulate window? What do you use? $\endgroup$
    – Moo
    Commented Feb 22, 2016 at 13:42
  • 2
    $\begingroup$ @Moo - that is one of my new favorite functions. I'm using the ManToGif function defined here $\endgroup$
    – Jason B.
    Commented Feb 22, 2016 at 13:44
  • $\begingroup$ Any ideas (cut and pasted his example) and get StringJoin::string: String expected at position 2 in charge<>Which[OperatingSystem==MacOSX,.mov,OperatingSystem==Windows,.avi]. >> Export::chtype: First argument charge<>Which[OperatingSystem==MacOSX,.mov,OperatingSystem==Windows,.avi] is not a valid file specification. >> Import::chtype: First argument $Failed is not a valid file, directory, or URL specification. >> Symbol::argx: Symbol called with 0 arguments; 1 argument is expected. >> $\endgroup$
    – Moo
    Commented Feb 23, 2016 at 1:54
  • 1
    $\begingroup$ @Moo - try the updated code I posted here instead $\endgroup$
    – Jason B.
    Commented Feb 23, 2016 at 16:59

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