From 54edf2cd1c45215d9bb9cc72e66f10814642f5ab Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 10 Sep 2018 21:27:32 +1000 Subject: [PATCH] physics cheatsheet - diffraction, huygen etc --- physics/final.aux | 4 +- physics/final.fdb_latexmk | 12 +- physics/final.fls | 14 ++ physics/final.log | 149 +++++++++++------- physics/final.pdf | Bin 547706 -> 595613 bytes physics/final.synctex.gz | Bin 49513 -> 53471 bytes physics/final.tex | 95 ++++++++--- .../graphics/bar-magnet-fields-rotated.png | Bin 0 -> 8022 bytes physics/graphics/bar-magnet-fields.png | Bin 0 -> 24755 bytes physics/graphics/diffraction-2.png | Bin 0 -> 4958 bytes physics/graphics/diffraction.jpg | Bin 0 -> 11577 bytes physics/graphics/grip.png | Bin 0 -> 13834 bytes physics/graphics/slap-2.jpeg | Bin 0 -> 7811 bytes physics/graphics/slap.png | Bin 0 -> 58305 bytes physics/waves-ref.tex | 89 +++++++++++ 15 files changed, 273 insertions(+), 90 deletions(-) create mode 100644 physics/graphics/bar-magnet-fields-rotated.png create mode 100644 physics/graphics/bar-magnet-fields.png create mode 100644 physics/graphics/diffraction-2.png create mode 100644 physics/graphics/diffraction.jpg create mode 100644 physics/graphics/grip.png create mode 100644 physics/graphics/slap-2.jpeg create mode 100644 physics/graphics/slap.png create mode 100644 physics/waves-ref.tex diff --git a/physics/final.aux b/physics/final.aux index 1202cb7..c4838dd 100644 --- a/physics/final.aux +++ b/physics/final.aux @@ -4,6 +4,4 @@ \@writefile{toc}{\contentsline {section}{\numberline {3}Fields and power}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}Waves}{}} \@writefile{toc}{\contentsline {section}{\numberline {5}Light and Matter}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Uncertainty principle}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Wave-particle duaity}{}} -\@writefile{toc}{\contentsline {section}{\numberline {6}Uncertainty}{}} +\@writefile{toc}{\contentsline {section}{\numberline {6}Experimental \\ design}{}} diff --git a/physics/final.fdb_latexmk b/physics/final.fdb_latexmk index c4a309f..117fbf7 100644 --- a/physics/final.fdb_latexmk +++ b/physics/final.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 3 -["pdflatex"] 1536458409 "final.tex" "final.pdf" "final" 1536458410 +["pdflatex"] 1536577652 "final.tex" "final.pdf" "final" 1536578664 "/usr/share/texmf-dist/fonts/map/fontname/texfonts.map" 1536122179 3332 103109f5612ad95229751940c61aada0 "" "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1536122179 1004 54797486969f23fa377b128694d548df "" "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1536122179 916 f87d7c45f9c908e672703b83b72241a3 "" @@ -12,6 +12,7 @@ "/usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1536122179 1324 c910af8c371558dc20f2d7822f66fe64 "" "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1536122179 1288 655e228510b4c2a1abe905c368440826 "" "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm" 1536122179 1292 296a67155bdbfc32aa9c636f21e91433 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmti10.tfm" 1536122179 1480 aa8e34af0eb6a2941b776984cf1dfdc4 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1536122179 34811 78b52f49e893bcba91bd7581cdc144c0 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1536122179 32080 340ef9bf63678554ee606688e7b5339d "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1536122179 30251 6afa5cb1d0204815a708a080681d4674 "" @@ -23,6 +24,7 @@ "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1536122179 32762 224316ccc9ad3ca0423a14971cfa7fc1 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1536122179 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1536122179 32716 08e384dc442464e7285e891af9f45947 "" + "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1536122179 37944 359e864bd06cde3b1cf57bb20757fb06 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb" 1536122179 31764 459c573c03a4949a528c2cc7f557e217 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb" 1536122179 34694 ad62b13721ee8eda1dcc8993c8bd7041 "" "/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1536122179 71627 94eb9990bed73c364d7f53f960cc8c5b "" @@ -64,18 +66,22 @@ "/usr/share/texmf-dist/web2c/texmf.cnf" 1536122179 33301 a3134070eacafb10b1f371612ce2650d "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1536231839 2755938 088f52af9b075e34d8f041b7c0f3de61 "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1536231814 7908118 f32434a9c220c6cf9671b5460a5588cc "" - "final.aux" 1536458410 611 39cbfdf8145bc0b5c6795cecc7ad4afd "" - "final.tex" 1536458409 15313 d18924719eb9ed94e763dc101c964318 "" + "final.aux" 1536577653 449 44f099e6311c1749bce1e3a7d9d76c9a "" + "final.tex" 1536578664 16981 42004f5b1161645833b0e01cb6530f72 "" "graphics/ac-generator.png" 1536455944 28991 f74a831edcaed66632e709a6b2e2ebfd "" "graphics/ac-motor.png" 1536455944 18626 d0f4943be26fdce44a4ce45ccb01633c "" "graphics/banked-track.png" 1536455944 51228 cc5d8f3f8efb06a64aca4afabfd63eed "" "graphics/circ-forces.png" 1536456196 17259 bc7cee5c5abcaea13025f490d4a700af "" "graphics/dc-motor-2.png" 1536455944 53769 fc78422983cc0333d421ae3c4a8e8e14 "" + "graphics/diffraction-2.png" 1536577616 4958 3b2c6e7ab542a52d65685a588f3b3b46 "" + "graphics/diffraction.jpg" 1536574120 11577 2cafc2e7bb89897fc6739c47a3d6db19 "" "graphics/field-lines.png" 1529318258 13526 3230dbcdb592145e128b7e3f27f400ba "" + "graphics/grip.png" 1536577088 13834 f2207261d5b4714f1d11704af5ca7376 "" "graphics/longitudinal-waves.png" 1531716387 71413 37bc678fd90369b170077578a70db4c4 "" "graphics/polarisation.png" 1534233118 19650 5282bd2bbad69802e09e7d936e5e988b "" "graphics/projectile-motion.png" 1536455944 53128 73ac7f2c98d2d1322c2b7390ef77f5ea "" "graphics/refraction.png" 1531719264 112546 1d6da3b03c7a31a9692d71fa6822c032 "" + "graphics/slap-2.jpeg" 1536577180 7811 874f42a4c2d07c949ba8d5d1c5a0d9c7 "" "graphics/transverse-waves.png" 1531716441 50968 31ae341ae41e85dcef4e5fdbea9a6e1c "" (generated) "final.pdf" diff --git a/physics/final.fls b/physics/final.fls index 8d8874f..ef09677 100644 --- a/physics/final.fls +++ b/physics/final.fls @@ -107,6 +107,12 @@ INPUT /var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map INPUT graphics/field-lines.png INPUT ./graphics/field-lines.png INPUT ./graphics/field-lines.png +INPUT graphics/slap-2.jpeg +INPUT ./graphics/slap-2.jpeg +INPUT ./graphics/slap-2.jpeg +INPUT graphics/grip.png +INPUT ./graphics/grip.png +INPUT ./graphics/grip.png INPUT graphics/ac-generator.png INPUT ./graphics/ac-generator.png INPUT ./graphics/ac-generator.png @@ -125,9 +131,16 @@ INPUT ./graphics/transverse-waves.png INPUT graphics/polarisation.png INPUT ./graphics/polarisation.png INPUT ./graphics/polarisation.png +INPUT graphics/diffraction.jpg +INPUT ./graphics/diffraction.jpg +INPUT ./graphics/diffraction.jpg +INPUT graphics/diffraction-2.png +INPUT ./graphics/diffraction-2.png +INPUT ./graphics/diffraction-2.png INPUT graphics/refraction.png INPUT ./graphics/refraction.png INPUT ./graphics/refraction.png +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmti10.tfm INPUT final.aux INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb @@ -140,5 +153,6 @@ INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb +INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb diff --git a/physics/final.log b/physics/final.log index caca239..a71eeae 100644 --- a/physics/final.log +++ b/physics/final.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.9.6) 9 SEP 2018 12:00 +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.9.6) 10 SEP 2018 21:07 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -260,21 +260,21 @@ Package amsmath Warning: Foreign command \over; File: graphics/circ-forces.png Graphic file (type png) -Package pdftex.def Info: graphics/circ-forces.png used on input line 69. +Package pdftex.def Info: graphics/circ-forces.png used on input line 71. 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(pdftex.def) Requested size: 175.02203pt x 99.58464pt. -Overfull \hbox (10.97217pt too wide) in paragraph at lines 358--359 +Overfull \hbox (10.97217pt too wide) in paragraph at lines 399--400 [] [] -./final.tex:406: Missing $ inserted. +./final.tex:450: Missing $ inserted. $ -l.406 E_ +l.450 E_ {\operatorname{k-max}}=hf - \phi I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. -./final.tex:407: Missing $ inserted. +./final.tex:451: Missing $ inserted. $ -l.407 +l.451 I've inserted a begin-math/end-math symbol since I think you left one out. 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zMYQHLr2@)nI2=fclOHRCYj-iWq1_}`RCAyz8(p8Hnt-TmdUrxhiw-Z^$&Ow|X7`nw zv;nmSWOCe1q}qQd0 U4thH~W`C!=Z51~CLKjk((DF6Tf diff --git a/physics/final.tex b/physics/final.tex index d988bac..998e2a5 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -24,17 +24,17 @@ % +++++++++++++++++++++++ \section{Motion} - $\operatorname{m/s} \times 3.6 = \operatorname{km/h}$ + $\operatorname{m/s} \, \times \, 3.6 = \operatorname{km/h}$ \subsection*{Inclined planes} - $F = m g \sin\theta F_{frict} = m a$ + $F = m g \sin\theta - F_{\text{frict}} = m a$ % ----------------------- \subsection*{Banked tracks} \includegraphics[height=4cm]{graphics/banked-track.png} - $$\theta = \tan^{-1} {{v^2} \over rg}$$ + $\theta = \tan^{-1} {{v^2} \over rg}$ $\Sigma F$ always acts towards centre, but not necessarily horizontally @@ -42,6 +42,8 @@ Design speed $v = \sqrt{gr\tan\theta}$ + $n\sin \theta = {mv^2 \div r}, \quad n\cos \theta = mg$ + % ----------------------- \subsection*{Work and energy} @@ -117,12 +119,13 @@ $F=-kx$ - $E_{elastic} = {1 \over 2}kx^2$ + $\text{elastic potential energy} = {1 \over 2}kx^2$ % ----------------------- \subsection*{Motion equations} \begin{tabular}{ l r } + & no \\ $v=u+at$ & $x$ \\ $x = {1 \over 2}(v+u)t$ & $a$ \\ $x=ut+{1 \over 2}at^2$ & $v$ \\ @@ -151,7 +154,7 @@ 2. Speed of light $c$ is the same to all observers (Michelson-Morley) - $\therefore , t$ must dilate as speed changes + $\therefore \, t$ must dilate as speed changes {\bf Inertial reference frame} $a=0$ @@ -220,6 +223,7 @@ \end{itemize} \includegraphics[height=2cm]{graphics/field-lines.png} + % \includegraphics[height=2cm]{graphics/bar-magnet-fields-rotated.png} % ----------------------- \subsection*{Gravity} @@ -276,7 +280,11 @@ \textbf{Right hand grip:} thumb points to $I$ (single wire) or N (solenoid / coil) - \textbf{Right hand slap:} $B \perp I \perp F$ + \includegraphics[height=2cm]{graphics/slap-2.jpeg} + \includegraphics[height=3cm]{graphics/grip.png} + + % \textbf{Right hand slap:} $B \perp I \perp F$ \\ + % ($I$ = thumb) \textbf{Flux-time graphs:} $m \times n = \operatorname{emf}$ @@ -325,14 +333,16 @@ % \end{wrapfigure} \textbf{AC:} slip ring (separate rings with constant contact) +% \pagebreak + % +++++++++++++++++++++++ \section{Waves} - \textbf{nodes:} fixed on graph - \textbf{amplitude:} max displacement from $y=0$ - \textbf{rarefactions} (expansions) / \textbf{compressions} - \textbf{mechanical:} transfer of energy without net transfer of matter - + \textbf{nodes:} fixed on graph \\ + \textbf{amplitude:} max disp. from $y=0$ \\ + \textbf{rarefactions} and \textbf{compressions} \\ + \textbf{mechanical:} transfer of energy without net transfer of matter \\ + \textbf{Longitudinal (motion $||$ wave)} \includegraphics[width=6cm]{graphics/longitudinal-waves.png} @@ -341,7 +351,6 @@ \includegraphics[width=6cm]{graphics/transverse-waves.png} % ----------------------- - \subsection*{Motors} $T={1 \over f}\quad$(period: time for one cycle) $v=f \lambda \quad$(speed: displacement / sec) @@ -351,22 +360,53 @@ % ----------------------- \subsection*{Interference} - When a medium changes character, energy is reflected, absorbed, and transmitted + + + + \textbf{Standing waves} - constructive int. at resonant freq + + \subsection*{Harmonics} + + + \(\lambda = {{al} \div n}\quad\) (\(\lambda\) for \(n^{th}\) harmonic)\\ + \(f = {nv \div al}\quad\) (\(f\) for \(n_{th}\) harmonic at length + \(l\) and speed \(v\)) \\ + where \(a=2\) for antinodes at both ends, \(a=4\) for antinodes at one end % ----------------------- \subsection*{Polarisation} \includegraphics[height=3.5cm]{graphics/polarisation.png} + % ----------------------- + \subsection*{Diffraction} + \includegraphics[width=6cm]{graphics/diffraction.jpg} + \includegraphics[width=6cm]{graphics/diffraction-2.png} + \begin{itemize} + \item \(pd = |S_1P-S_2P|\) for \(p\) on screen + \item Constructive: \(pd = n\lambda, n \in \mathbb{Z}\) + \item Destructive: \(pd = (n-{1 \over 2})\lambda, n \in \mathbb{Z}\) + \item Fringe separation: \(\Delta x = {{\lambda l }\over d}\) where \\ + \(\Delta x\) = fringe spacing \\ + \(l\) = distance from slits to screen\\ + \(d\) = slit separation (\(=S_1-S_2\)) + \item significant diffraction when ${\lambda \over \Delta x} \ge 1$ + \end{itemize} + + + % ----------------------- \subsection*{Refraction} \includegraphics[height=3.5cm]{graphics/refraction.png} - Angle of incidence $\theta_i =$ angle of reflection $\theta_r$ + When a medium changes character, energy is \emph{reflected}, \emph{absorbed}, and \emph{transmitted} + + angle of incidence $\theta_i =$ angle of reflection $\theta_r$ Critical angle $\theta_c = \sin^-1{n_2 \over n_1}$ Snell's law $n_1 \sin \theta_1=n_2 \sin \theta_2$ + % +++++++++++++++++++++++ \section{Light and Matter} @@ -416,7 +456,7 @@ $V=h_{\text{eV}}(f-f_0)$ - \columnbreak + % \columnbreak \subsection*{De Broglie's theory} @@ -447,13 +487,13 @@ \item No. of lines - include all possible states \end{itemize} - \subsection{Uncertainty principle} + \subsection*{Uncertainty principle} measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. - \subsection{Wave-particle duaity} + \subsection*{Wave-particle duaity} - wave model: + \subsubsection*{wave model} \begin{itemize} \item cannot explain photoelectric effect \item $f$ is irrelevant to photocurrent @@ -461,7 +501,7 @@ \item speed depends on medium \end{itemize} - particle model: + \subsubsection*{particle model} \begin{itemize} \item explains photoelectric effect @@ -470,20 +510,21 @@ \item double slit: photons interact. interference pattern still appears when a dim light source is used so that only one photon can pass at a time \item light exerts force \item light bent by gravity + \item quantised energy \end{itemize} % +++++++++++++++++++++++ - \section{Uncertainty} + \section{Experimental \\ design} - \textbf{Absolute uncertainty} - $\Delta$ - same units as quantity. + \textbf{Absolute uncertainty} $\Delta$ \\ + (same units as quantity) \[ \Delta(m) = {{\mathcal{E}(m)} \over 100} \cdot m \] - \[ (A \pm \Delta A) + (B \pm \Delta A) = (A+B) \pm (\Delta A + \Delta B) \] \[ (A \pm \Delta A) - (B \pm \Delta A) = (A-B) \pm (\Delta A + \Delta B) \] \[ c(A \pm \Delta A) = cA \pm c \Delta A \] - \textbf{Relative uncertainty} - $\mathcal{E}$ - unitless. - \[ \mathcal{E}(m) = {{\Delta(m)} \over m} \cdot 100} \] + \textbf{Relative uncertainty} $\mathcal{E}$ (unitless) + \[ \mathcal{E}(m) = {{\Delta(m)} \over m} \cdot 100 \] \[ (A \pm \mathcal{E} A) \cdot (B \pm \mathcal{E} B) = (A \cdot B) \pm (\mathcal{E} A + \mathcal{E} B) \] \[ (A \pm \mathcal{E} A) \div (B \pm \mathcal{E} B) = (A \div B) \pm (\mathcal{E} A + \mathcal{E} B) \] \[ (A \pm \mathcal{E} A)^n = (A^n \pm n \mathcal{E} A) \] @@ -494,8 +535,9 @@ \textbf{Precision} - concordance of values \\ \textbf{Accuracy} - closeness to actual value + \columnbreak - + \quad @@ -503,4 +545,7 @@ \end{multicols} + +% \includegraphics[height=5cm]{graphics/em-spectrum.png} + \end{document} diff --git a/physics/graphics/bar-magnet-fields-rotated.png b/physics/graphics/bar-magnet-fields-rotated.png new file mode 100644 index 0000000000000000000000000000000000000000..956d545602e3d33d7c716100dc726d10a73188be GIT binary patch literal 8022 zcmV-cAF1GpP)O007?z0{{R3>%nJ>00004XF*Lt006O% z3;baP0000WV@Og>004R>004l5008;`004mK004C`008P>0026e000+ooVrmw00093 zP)t-s{{H^J*XonH+J&#x&*1Ow^!RtC(NT)RMt{69WUgwR%sqCuHf^)9%;jB^$KLAm zqQl=ufxRJTMyEJOD-|O^Cgury9&oykaNQ1pni^4i{wliq3aG}n7snV**;xcBhp26NYaI}7_ z)5F;7H*d66jl?^2wg3PC3mhsLI9(=AhA&{LEncG^L2n^OcPdwv5F|PmF;gpAoLE>| zR#;#~UWqkhsz6|qR9R;`Vx3Q0b3$K^QCn^~VxnJJp^Zn2vN3eSA7t1V-#pd?-{``G@er9~5!s+?n`u?%o^ju|z{{Hv<{`UU<__oa4{r>du z)S-85W5?O+{{H#<^T+-E@~Xqx@SAk-n|AS>n)u)8{rvCv+py{L_~p~YXINTdYkc

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+\section{Waves}\label{waves}} + +\hypertarget{longitudinal-motion-wave}{% +\subsection{\texorpdfstring{Longitudinal (motion \(||\) +wave)}{Longitudinal (motion \textbar{}\textbar{} wave)}}\label{longitudinal-motion-wave}} + +\textbf{rarefactions} (expansions) and \textbf{compressions} + +\includegraphics{graphics/longitudinal-waves.png} + +\hypertarget{transverse-waves-motion-perp-wave}{% +\subsection{\texorpdfstring{Transverse waves (motion \(\perp\) +wave)}{Transverse waves (motion \textbackslash{}perp wave)}}\label{transverse-waves-motion-perp-wave}} + +\textbf{nodes} are fixed on graph + +\includegraphics{graphics/transverse-waves.png} + +\hypertarget{measuring-mechanical-waves}{% +\subsection{Measuring mechanical +waves}\label{measuring-mechanical-waves}} + +\textbf{Amplitude \(A\)} - max displacement from rest position\\ +\textbf{Wavelength \(\lambda\)} - \(x\) distance between \(y_1=y_2\)\\ +\textbf{Frequency \(f\)} - number of cycles (wavelengths) per second + +\(T={1 \over f}\quad\)(period: time for one cycle)\\ +\(v=f \lambda \quad\)(speed: displacement per second) + +\hypertarget{doppler-effect}{% +\subsection{Doppler effect}\label{doppler-effect}} + +When \(P_1\) approaches \(P_2\), each wave \(w_n\) has slightly less +distance to travel than \(w_{n-1}\). Hence, \(w_n\) reaches the observer +sooner than \(w_{n-1}\), increasing ``apparent'' wavelength. + +\hypertarget{interference}{% +\subsection{Interference}\label{interference}} + +When a medium changes character, energy is \emph{reflected}, +\emph{absorbed}, and \emph{transmitted} + +\textbf{Standing waves} - constructive int. at resonant freq + +\hypertarget{polarisation}{% +\subsection{Polarisation}\label{polarisation}} + +\includegraphics[width=0.2\textwidth,height=\textheight]{graphics/polarisation.png} + +\hypertarget{refraction}{% +\subsection{Refraction}\label{refraction}} + +\includegraphics{graphics/refraction.png} + +Angle of incidence \(\theta_i =\) angle of reflection \(\theta_r\) + +Critical angle \(\theta_c = \sin^-1{n_2 \over n_1}\) + +Snell's law - \(n_1 \sin \theta_1=n_2 \sin \theta_2\) + +\hypertarget{harmonics}{% +\subsection{Harmonics}\label{harmonics}} + +where \(a=2\) for antinodes at both ends, \(a=4\) for antinodes at one +end: + +\(\lambda = {{al} \div n}\quad\) (wavelength for \(n^{th}\) harmonic)\\ +\(f = {nv \div al}\quad\) (frequency for \(n_{th}\) harmonic at length +\(l\) and speed \(v\)) + +\hypertarget{double-split}{% +\subsection{Double split}\label{double-split}} + +Path difference \(pd = |S_1P-S_2P|\) for point \(p\) on screen + +Constructive: \(pd = n\lambda\) where \(n \in [0, 1, 2, ...]\)\\ +Destructive: \(pd = (n-{1 \over 2})\lambda\) where +\(n \in [1, 2, 3, ...]\) + +Fringe separation: \(\Delta x = {{\lambda l }\over d}\) + +where \(\Delta x\) is distance between fringes\\ +\(l\) is distance from slits to screen\\ +\(d\) is separation between sluts (\(=S_1-S_2\)) + +\includegraphics[width=\textwidth,height=1.04167in]{graphics/em-spectrum.png} -- 2.47.1