File:Caustics.gif
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Summary
| Description |
English: When light is refracted from a non-flat surface, it simply happens that there are regions where more rays are passing through, creating very bright spots (or lines) called "caustics". |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1229743952594640897 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
n = 2; (*Refractive index of the bottom medium*)
z = 5; (*The bottom of the plot is at zero. This set how high you want to plot*)
h[x_] := 1 + 0.03 Cos[x] + 0.1 Sin[2.1 x] + 0.11 Sin[2.8 x]; (*profile of the refractive medium*)
dh[x_] := Evaluate[D[h[x], x]]; (*Derivative of the profile (that locally determines how Snell law works*)
R[x_] := x + (z - h[x]) dh[x] (n Sqrt[1 - (n^2 - 1) dh[x]^2] - 1)/(1 - (n^2 - 1) dh[x]^2); (*Where the ray ends up*)
Show[
Plot[h[x], {x, 0, 2 \[Pi]}, Background -> Black, PlotStyle -> {Gray}, Filling -> Axis, PlotRange -> {0, z}, Axes -> False, FillingStyle -> Gray],
Graphics[{
Yellow, Thick, Opacity[0.1], Table[{Line[{{y, 0}, {y, h[y]}}], Line[{{y, h[y]}, If[Im[R[y]] == 0, {R[y], z}, {y, h[y]}]}]}, {y, 0, 2 \[Pi], 0.02}]
}]
, ImageSize -> Large
] (*Plot of the caustics*)
(*Generate the animation*)
listy = RandomSample@Table[y, {y, 0, 2 \[Pi], 0.015}]; (*Randomize the order the rays appear*)
dim = Dimensions[listy][[1]];
p1 = Table[
Show[
Plot[h[x], {x, 0, 2 \[Pi]}, Background -> Black, PlotStyle -> {Gray}, Filling -> Axis, PlotRange -> {0, z}, Axes -> False, FillingStyle -> Gray],
Graphics[{
Yellow, Thick, Opacity[0.15], Table[{Line[{{y, 0}, {y, h[y]}}], Line[{{y, h[y]}, If[Im[R[y]] == 0, {R[y], z}, {y, h[y]}]}]}, {y, listy[[1 ;; k]]}]
}]
, ImageSize -> Large ]
, {k, 1, dim, 2}]; (*Plot every two frames, otherwise the animation is too heavy*)
ListAnimate[p1]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:33, 19 February 2020 | | 576 × 356 (13.69 MB) | Berto | User created page with UploadWizard |
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