\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{Konrad\_Z (StudentKZ)} \pdfinfo{ /Title (aqa-a-level-physics-wave-particle-duality.pdf) /Creator (Cheatography) /Author (Konrad\_Z (StudentKZ)) /Subject (AQA A-level Physics: Wave-Particle Duality Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{0A0A0A} \definecolor{LightBackground}{HTML}{F7F7F7} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{AQA A-level Physics: Wave-Particle Duality Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Konrad\_Z (StudentKZ)} via \textcolor{DarkBackground}{\uline{cheatography.com/188038/cs/42189/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}Konrad\_Z (StudentKZ) \\ \uline{cheatography.com/studentkz} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 2nd February, 2024.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Newton's Corpuscles}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/studentkz_1706288449_download (6).png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Newton's Corpuscular Theory of Light}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Newton theorised light was made up of particles called corpuscles.} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Reflection caused by corpuscles colliding with surface and repulsive force pushing them back. Caused perpendicular component of velocity to change direction, the parallel component stays the same.} \tn % Row Count 6 (+ 4) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Refraction caused by corpuscles approaching denser medium. Short-range forces of attraction causes perpendicular component of velocity to increase, parallel component stays the same. Light bends towards normal.} \tn % Row Count 11 (+ 5) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{According to Newton's theory, light travels faster in denser mediums.} \tn % Row Count 13 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Huygen's Waves}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/studentkz_1706373008_resize-17063729881118007631resize1706372915186597731911.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Huygen's Wave Theory of Light}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Huygen theorised light was a wave, every point on a wavefront is a point source to secondary wavelets which spread out to form next wavefronts. This is Huygen's principle.} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Reflection caused by whole wavefront not reaching surface at once. Wavelets spread away from surface once they reach it and rejoin with others to form reflected wavefront.} \tn % Row Count 8 (+ 4) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Refraction caused by light entering more optically dense medium. This slows down light and makes it bend towards normal.} \tn % Row Count 11 (+ 3) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Newton's theory preferred over Huygen's because Newton had very high reputation at the time, diffraction had not yet been observed and the speed of light had not yet been measured.} \tn % Row Count 15 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Young's Double Slit Apparatus}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/studentkz_1706372457_resize-17063724391684655214download8.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Young's Double Slit Experiment}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Coherent light shone through two slits so that it diffracts. Each slit is a coherent point source making a pattern of light and dark fringes.} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Light fringes formed where light meets in phase and interferes constructively, occurs when path difference is a whole number of wavelengths.} \tn % Row Count 6 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Dark fringes formed where light meets completely out of phase and interferes destructively, occurs when path difference is a whole number plus half wavelengths.} \tn % Row Count 10 (+ 4) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{If Newton's theory was correct: Only two bright fringes corresponding to the two slits. Experiment demonstrated diffraction and interference, both properties only explained by Huygen's theory.} \tn % Row Count 14 (+ 4) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Even after experiment: Huygen's theory still wasn't accepted because Newton was a historical figure who scientists expected to be correct.} \tn % Row Count 17 (+ 3) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Newton's theory only disregarded after speed of light was measured in water, it was shown that light actually moves slower in denser substances contradicting the corpuscular theory.} \tn % Row Count 21 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Electromagnetic Waves}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/studentkz_1706372581_resize-1706372570356573878download9.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Maxwell's equation for EM waves}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Electromagnetic waves: alternating magnetic (B) and electric (E) fields travelling in phase and at right angles to each other. Direction of wave travel perpendicular to oscillations} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{Maxwell predicted EM waves existed: Theorised formula for their speed in a vaccum (c) before experiment evidence.} \tn % Row Count 7 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{c = 1 / sqrt(μ0ε0) \newline \newline c = Speed of Light (3x10\textasciicircum{}8\textasciicircum{} ms\textasciicircum{}-1\textasciicircum{}) \newline μ0 = Permeability of free space (4πx10\textasciicircum{}-7\textasciicircum{} Hm\textasciicircum{}-1\textasciicircum{}) \newline ε0 = Permittivity of free space (8.85x10\textasciicircum{}-12\textasciicircum{} Fm\textasciicircum{}-1\textasciicircum{})} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Hertz' Apparatus}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/studentkz_1706374435_download (10).png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Hertz' Radio Wave experiment}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Hertz discovered radio waves by using apparatus to allow sparks to jump across a gap of air.} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Dipole reciever detects electric field. Made by placing second set of charged plates parallel to those forming the voltage sparks.} \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Loop of wire with gap detects magnetic field as field enters loop causing change in magnetic flux inducing p.d causing spark to cross the gap in the wire.} \tn % Row Count 9 (+ 4) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Metal sheet in front apparatus, radio waves reflect back creating stationary waves. Use one of the detectors to find the distance between adjacent nodes to find the wavelength.} \tn % Row Count 13 (+ 4) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Wavelength multiplied by frequency of the waves to find speed of waves. Hertz's value same as Maxwell's therefore radio waves are EM waves.} \tn % Row Count 16 (+ 3) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Rotating reciever: Plane of detector perpendicular to EM waves produced maximum value. Plane of detector parallel to EM waves produces minimum value and no signal detected. Therefore radio waves are polarised.} \tn % Row Count 21 (+ 5) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}