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% Most of the following are not required for the majority
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% Document Info
\author{cadmiumium}
\pdfinfo{
  /Title (how-waves-explain-the-behaviour-of-light.pdf)
  /Creator (Cheatography)
  /Author (cadmiumium)
  /Subject (How waves explain the behaviour of light Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{How waves explain the behaviour of light Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{cadmiumium} via \textcolor{DarkBackground}{\uline{cheatography.com/135751/cs/28766/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}cadmiumium \\
  \uline{cheatography.com/cadmiumium} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 5th August, 2021.\\
   Updated 5th August, 2021.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




\begin{document}
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% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
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\begin{multicols*}{3}

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\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Formulas}}  \tn
% Row 0
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{\bf{f=1/T}} & {\bf{v=fλ}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
{\bf{λ=c/f}} & {\bf{v=λ/T}} \tn 
% Row Count 2 (+ 1)
% Row 2
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{\emph{constructive}} p.d (antinode) = {\bf{nλ}} & 'loud', 'light band' \tn 
% Row Count 4 (+ 2)
% Row 3
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\mymulticolumn{2}{x{5.377cm}}{or {\bf{nλ = |S₁X-S₂X|}}} \tn 
% Row Count 5 (+ 1)
% Row 4
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{\emph{destructive}} p.d (node) = {\bf{(n-0.5)λ}} & 'quiet', 'dark band' \tn 
% Row Count 7 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{or {\bf{(n-0.5)λ = |S₁X-S₂X|}}} \tn 
% Row Count 8 (+ 1)
% Row 6
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one free end, one fixed (odd): & {\bf{λ=4L/n}}, {\bf{f=nv/4L}} \tn 
% Row Count 10 (+ 2)
% Row 7
\SetRowColor{white}
fixed ends: & {\bf{λ=2L/n}}, {\bf{f=nv/2L}} \tn 
% Row Count 12 (+ 2)
% Row 8
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fringe spacing: & {\bf{∆x=λL/d}} \tn 
% Row Count 13 (+ 1)
% Row 9
\SetRowColor{white}
bigger Δx gives more refraction, more spread out & \textasciicircum{}Δx=fringe spacing (m), λ=wavelength (m), L=distance from slits to screen (m), d=slit separation (m)\textasciicircum{} \tn 
% Row Count 19 (+ 6)
% Row 10
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refraction \& reflection: & {\bf{n=c/v}} \tn 
% Row Count 21 (+ 2)
% Row 11
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where; n=speed of light in a vacuum/ speed of light medium & {\bf{n₁v₁=n₂v₂}} \tn 
% Row Count 24 (+ 3)
% Row 12
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diffraction∝λ/w & {\bf{n₁sin(θ₁)=n₂sin(θ₂)}} \tn 
% Row Count 26 (+ 2)
% Row 13
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energy∝frequency & {\bf{n₁sin(θ₁)=n₂}} \tn 
% Row Count 28 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Young's double slit experiment}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Young's double slit experiment shows light exhibiting the wave properties of diffraction and interference.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Light can be polarised, observed as white light diffracts and colours are seen as a result. As only transverse waves can be polarised, the wave model of light is proven.} \tn 
% Row Count 7 (+ 4)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Snell's Law}}  \tn
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\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{n₁=refractive index of first medium \newline θ₁=angle to the normal in first medium  \newline n₂=refractive index of second medium \newline θ₂=angle to the normal in second medium}  \tn 
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\par\addvspace{1.3em}

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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave types}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{{\emph{Transverse waves:}} particle moves along {\bf{vertical}} axis} \tn 
% Row Count 2 (+ 2)
% Row 1
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% Row Count 4 (+ 2)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{{\emph{Coherent waves:}} waves with the {\bf{same frequency}}} \tn 
% Row Count 6 (+ 2)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{Mechanical (sound, air, water) waves do not exist in a vacuum, they {\bf{require a medium to travel through}}} \tn 
% Row Count 9 (+ 3)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Electromagnetic (light) waves can exist in a vacuum, {\bf{do not require a medium}}} \tn 
% Row Count 11 (+ 2)
% Row 5
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Travelling wave:}} a wave for which the crests and troughs travel in the direction of wave propagation.} \tn 
% Row Count 14 (+ 3)
% Row 6
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Standing Waves:}} when 2 wave trains with the same amplitude and wavelength move through each other, the resulting interfering pattern results in a standing wave. Consists of alternating nodes and antinodes that remain in a fixed position, wave appears to be stationary/'standing'} \tn 
% Row Count 20 (+ 6)
% Row 7
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\mymulticolumn{1}{x{5.377cm}}{fundamental frequency: {\bf{n=1}}} \tn 
% Row Count 21 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{{\emph{formation of standing waves on a string: }} \newline 1. waves {\bf{reflect}} at both ends of string \newline 2. reflections travel in opposite directions with the same frequency and amplitude \newline 3. fixed ends are {\bf{nodes}}, free ends are {\bf{antinodes}}}  \tn 
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Constructive Interference:}} When waves in the same phase overlap, their amplitudes add together \newline {\bf{Destructive Interference:}} When waves of different phases overlap, their amplitudes cancel \newline {\bf{Nodes:}} Points of complete destructive interference \newline {\bf{Antinodes:}} Points of complete constructive interference, largest amplitude}  \tn 
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave resonance}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Waves reflect at the end of a string and are {\bf{inverted}} if end is fixed} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{An object or system will resonate if driven at its {\bf{natural}} frequency} \tn 
% Row Count 4 (+ 2)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Resonance greatly increases magnitude of oscillation in an object/system} \tn 
% Row Count 6 (+ 2)
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Doppler effect}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Doppler effect is the detected frequency change due to the relative motion between a wave source and detector.} \tn 
% Row Count 3 (+ 3)
% Row 1
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{f decreases when source and detector move away from each other} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Doppler effect:}}  \tn
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Polarising filters}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Image could not be loaded.} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Waves}}  \tn
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Variables}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{independent: variable that is being changed (x-axis)} \tn 
% Row Count 2 (+ 2)
% Row 1
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% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}