Rainbow from droplet

Explaining rainbows with refraction and internal reflection, including pileup at angle 42°.

optics_rainbow-001.pngoptics_rainbow-002.pngoptics_rainbow-003.pngoptics_rainbow-004.pngoptics_rainbow-005.png

Edit and compile if you like:

% Author: Izaak Neutelings (June 2020)
% Inspiration:
% https://www.researchgate.net/figure/a-Refractive-index-and-b-dispersion-of-bulky-soft-glasses-NC21-LLF1-SF6-and-F2-As_fig1_236110630
% https://link.springer.com/article/10.1007/s11082-014-9979-y
\documentclass[border=3pt,tikz]{standalone}
\usepackage{siunitx}
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{fadings}
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\usetikzlibrary{decorations.pathreplacing} % for curly braces
\tikzset{>=latex} % for LaTeX arrow head
\contourlength{1.7pt}
\newcommand\degree{^\circ}
\colorlet{myblue}{blue!80!black}
\colorlet{myred}{black!50!red}
\colorlet{watercol}{blue!70!cyan!50}
\tikzstyle{myarr}=[-{Latex[length=3,width=2]}]
\tikzstyle{water}=[ball color=watercol]
\tikzset{
beam/.style={very thick,line cap=round,line join=round},
}
\begin{document}
% DROPLET refraction & reflection
\begin{tikzpicture}
\def\L{2.4} % length of ray outside droplet
\def\R{1.8} % droplet radius
\def\na{1.0} % air
\def\nw{1.33} % water
\def\alphI{150} % A: incident (180-90)
\pgfmathsetmacro\thetI{180-\alphI} % theta_1: incident
\pgfmathsetmacro\thetII{asin(\na/\nw*sin(\thetI)} % theta_2: air -> water & reflection
\pgfmathsetmacro\alphII{\alphI+2*\thetII-180} % C: reflected
 
 
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Click to download: optics_rainbow.texoptics_rainbow.pdf
Open in Overleaf: optics_rainbow.tex

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