From: Andrew Lorimer Date: Wed, 26 Sep 2018 12:36:43 +0000 (+1000) Subject: update physics cheatsheet X-Git-Tag: yr11~34 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/20fa557acc8f0e3043b8334146f89be60234cb93?ds=sidebyside update physics cheatsheet --- diff --git a/physics/final.fls b/physics/final.fls deleted file mode 100644 index ef09677..0000000 --- a/physics/final.fls +++ /dev/null @@ -1,158 +0,0 @@ -PWD /home/andrew/notes/physics -INPUT /usr/share/texmf-dist/web2c/texmf.cnf -INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt -INPUT final.tex -OUTPUT final.log -INPUT /usr/share/texmf-dist/tex/latex/base/article.cls -INPUT /usr/share/texmf-dist/tex/latex/base/article.cls -INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo -INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo -INPUT /usr/share/texmf-dist/tex/latex/tools/multicol.sty -INPUT /usr/share/texmf-dist/tex/latex/tools/multicol.sty -INPUT /usr/share/texmf-dist/tex/latex/preprint/fullpage.sty -INPUT 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--git a/physics/final.tex b/physics/final.tex index 6e10af0..d9766f6 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -9,6 +9,8 @@ \usepackage{graphicx} \usepackage{wrapfig} \usepackage{enumitem} +\usepackage{supertabular} +\usepackage{tabularx} \setitemize{noitemsep,topsep=0pt,parsep=0pt,partopsep=0pt,leftmargin=5pt} @@ -82,8 +84,9 @@ % ----------------------- \subsection*{Projectile motion} \begin{itemize} - \item{horizontal component of velocity is constant if no air resistance} - \item{vertical component affected by gravity: $a_y = -g$} + \item $v_x$ is constant: $v_x = {s \over t}$ + \item use suvat to find $t$ from $y$-component + \item vertical component gravity: $a_y = -g$ \end{itemize} \begin{align*} @@ -370,6 +373,9 @@ % ----------------------- \subsection*{Interference} + \includegraphics[width=4.5cm]{graphics/possons-spot.png} + Poissons's spot supports wave theory (circular diffraction) + \textbf{Standing waves} - constructive int. at resonant freq \textbf{Coherent } - identical frequency, phase, direction (ie strong & directional). e.g. laser @@ -377,6 +383,9 @@ \textbf{Incoherent} - e.g. incandescent bulb + + + % ----------------------- \subsection*{Harmonics} @@ -401,12 +410,12 @@ % \(\Delta x\) = fringe spacing \\ \(l\) = distance from source to observer\\ \(d\) = separation between each wave source (e.g. slit) \(=S_1-S_2\) + \item diffraction $\propto {\lambda \over d}$ \item significant diffraction when ${\lambda \over \Delta x} \ge 1$ \item diffraction creates distortion (electron $>$ optical microscopes) \end{itemize} - % ----------------------- \subsection*{Refraction} \includegraphics[height=3.5cm]{graphics/refraction.png} @@ -438,57 +447,72 @@ % ={P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} % \end{align*} + \subsection*{De Broglie's theory} + + \[ \lambda = {h \over \rho} = {h \over mv} \] + \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \] + \begin{itemize} + \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$) + \item confirmed by e- and x-ray patterns + \end{itemize} + + \subsection*{X-ray electron interaction} + + \begin{itemize} + \item e- stable if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ + \item $\therefore 2\pi r = n{h \over mv} = n \lambda$ (circumference) + \item if $2\pi r \ne n{h \over mv}$, no standing wave + \item if e- = x-ray diff patterns, $E_{\text{e-}}={\rho^2 \over 2m}={({h \over \lambda})^2 \div 2m}$ + % \item calculating $h$: $\lambda = {h \over \rho}$ + \end{itemize} + \subsection*{Photoelectric effect} \begin{itemize} \item $V_{\operatorname{supply}}$ does not affect photocurrent - \item $V_{\operatorname{sup}} > 0$: e- attracted to collector anode - \item $V_{\operatorname{sup}} < 0$: attracted to illuminated cathode, $I\rightarrow 0$ - \item $v$ of depends on ionisation energy (shell) + \item $V_{\operatorname{sup}} > 0$: attracted to +ve + \item $V_{\operatorname{sup}} < 0$: attracted to -ve, $I\rightarrow 0$ + \item $v$ of e- depends on shell \item max current depends on intensity \end{itemize} - \textbf{Threshold frequency $f_0$} + \subsubsection*{Threshold frequency $f_0$} - Minimum $f$ for photoelectrons to be ejected. $x$-intercept of frequency vs $E_K$ graph. if $f < f_0$, no photoelectrons are detected. + min $f$ for photoelectron release. if $f < f_0$, no photoelectrons. - \textbf{Work function $\phi$} + \subsubsection*{Work function $\phi=hf_0$} - Minimum $E$ required to release photoelectrons. Magnitude of $y$-intercept of $f$ vs $E_K$ graph. $\phi$ is determined by strength of bonding. Units: eV or J. + min $E$ for photoelectron release. determined by strength of bonding. Units: eV or J. - $\phi=hf_0$ + \subsubsection*{Kinetic energy E_K=hf - \phi = qV_0} - \textbf{Kinetic energy} - E_{\operatorname{k-max}}=hf - \phi + $V_0 = E_K$ in eV \\ + % $E_K = x$-int of $V\cdot I$ graph (in eV) \\ + dashed line below $E_K=0$ - voltage in circuit or stopping voltage = max $E_K$ in eV \\ - $E_K = x$-int of $V\cdot I$ graph (in eV) \\ - dashed line below $E_K=0$ ($E_K < 0$ is impossible) + \subsubsection*{Stopping potential $V_0$ for min $I$} - \textbf{Stopping potential $V$ for min $I$} + $$V_0=h_{\text{eV}}(f-f_0)$$ - $V=h_{\text{eV}}(f-f_0)$ + \subsubsection*{Graph features} - \subsection*{De Broglie's theory} + \newcolumntype{b}{>{\hsize=.75\hsize}X} +\newcolumntype{s}{>{\hsize=.3\hsize}X} - \[ \lambda = {h \over \rho} = {h \over mv} \] - \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \] - \begin{itemize} - \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$) - \item confirmed by similar e- and x-ray diff patterns - \end{itemize} + \begin{tabularx}{\columnwidth}{bbbb} +\hline +&$m$&$x$-int&$y$-int \\ +\hline +\hline +$f \cdot E_K$ & $h$ & $f_0$ & $-\phi$ \\ +$V \cdot I$ & & $V_0$ & intensity\\ +$f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & +\hline +\end{tabularx} - \subsection*{X-ray electron interaction} - \begin{itemize} - \item e- is only stable if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ - \item rearranging this, $2\pi r = n{h \over mv} = n \lambda$ (circumference) - \item if $2\pi r \ne n{h \over mv}$, no standing wave - \item if e- = x-ray diff patterns, $E_{\text{e-}}={\rho^2 \over 2m}={({h \over \lambda})^2 \div 2m}$ - \item calculating $h$: $\lambda = {h \over \rho}$ - \end{itemize} \subsection*{Spectral analysis} @@ -512,6 +536,7 @@ \item $f$ is irrelevant to photocurrent \item predicts delay between incidence and ejection \item speed depends on medium + \item supported by bright spot in centre \end{itemize} \subsubsection*{particle model}