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z6qGbpU3cX&ytLfTEbIIC@8#|uTmR3iTh|}$weZlp=V=c<e0<m5e}Dc?;YTkv=Q6+@ z&B7tDLhE5mC?exSV+`gr9W8}95mTbmk#)f2Kw;TXa7YT7kL*MiF;M|Ool|R#k^ByG zKG-}5i$r*dg(3lRL^l_Qy4cfelF*b55&~<2F%;%(V8hS^Rnh3m+9KRt^tuPdIY_Dn z{34j4YB9_|u!!kUr|ZsAH<(T6fy1G`2166fqJ%)khesCOu|g^~P>pF3z6Mi^D#0P3 zuwg|*K~iAeTv$Pc<X}h`AL7i$&;)Z`M2LgMMvd*~Ff_sZ`LM+lrWRrvOoEApV>FsU ji5WFwhGsN3{%4ly*x;9aPii9r0|SGntDnm{r-UW|hM<W} diff --git a/v0.1/em_waves.tex b/v0.1/em_waves.tex index 63c6ff2..7355365 100644 --- a/v0.1/em_waves.tex +++ b/v0.1/em_waves.tex @@ -1218,8 +1218,10 @@ wobei $E_{e0,p} = (E_{e0,x}^2 + E_{e0,y}^2)^{1/2}$ und $E_{r0,p}=(E_{r0,x}^2+E_{ Wir können jetzt die Fresnel-Gleichungen für die Reflektivitäten angeben: -$$ \rho_p = \frac{\tan (\alpha-\beta)}{\tan(\alpha+\beta)},$$ -$$\rho_s = -\frac{\sin(\alpha-\beta)}{\sin(\alpha+\beta)}.$$ +$$ \rho_p = \frac{n_2\cos\alpha - n_1\cos\beta}{n_2\cos\alpha+n_1\cos\beta} + = \frac{\tan (\alpha-\beta)}{\tan(\alpha+\beta)},$$ +$$\rho_s = \frac{n_1\cos\alpha-n_2\cos\beta}{n_1\cos\alpha+n_2\cos\beta} + = -\frac{\sin(\alpha-\beta)}{\sin(\alpha+\beta)}.$$ \textbf{Beispiel 1:} Reflexion an einer Wasseroberfläche, Kronglas\\ Für Wasser ist $n_2\approx 4/3$, für Kronglas ist $n_2\approx 3/2$. Weiterhin gilt für kleine Winkel $\sin\alpha\approx \alpha$ und $\sin\beta\approx \beta$, so dass für $n_1=1$ aus dem Snell'schen Gesetz @@ -1234,7 +1236,7 @@ Entsprechend ist für Wasser $\rho_s\approx -1/7$ und für Kronglas $\rho_s\appr Für den Fall, dass der Brechungswinkel $\beta=\pi/2$ wird, wird Reflektivität $\rho_s^2=\rho_p^2=1$. Diese Bedingung lässt sich nur erreichen, wenn wir einen Übergang von einem Medium $n_1>n_2$ betrachten. Die Bedingung an den minimalen Winkel $\alpha_g$, für den $\beta(\alpha_g)=\pi/2$ gilt, ergibt sich aus der Snell'schen Gleichung $$n_1 \sin\alpha_g = n_2,$$ -für den Übergang von Wasser ($n_1=4/3)$) zu Luft ($n_2=1$) erhalten wir +für den Übergang von Wasser ($n_1=4/3$) zu Luft ($n_2=1$) erhalten wir $$\sin\alpha_g = \frac{n_2}{n_1}\approx \frac{3}{4},$$ so dass für Wasser $\alpha_g\approx 49^\circ$ (für Kronglas ist $\alpha_g\approx 42^\circ$). @@ -1341,12 +1343,20 @@ ist und senkrecht hierzu haben wir einen davon unterschiedlichen Brechungsindex Fällt eine ebene Welle senkrecht auf eine Grenzschicht zu einem positiven, uniaxialen Kristall, spaltet sich der Strahl in einen \textit{gewöhnlichen} und einen außergewöhnlichen Strahl auf, deren Polarisationsrichtungen den Richtungen von $n_O$ und $n_a$ entsprechen. Der gewöhnliche Strahl folgt dem Snell'schen Brechungsgesetz und ist senkrecht polarisiert zu der Polarisationsrichtung des außergewöhnlichen Strahls, der nicht dem Snell'schen Gesetz folgt, sondern auch bei senkrechtem Auftreffen in einem Winkel zum gewöhnlichen Strahl propagiert. \textit{Zum Nachdenken: Konstruieren Sie den Verlauf der Elementarwellen des außergewöhnlichen Strahls - berücksichtigen Sie hierbei die unterschiedliche Ausbreitungsgeschwindigkeit.} +Anwendungen für die Doppelbrechung: +\begin{itemize} + \item \textit{Nicol}-Prisma: Das Phänomen der Doppelbrechung kann dazu genutzt werden, um Licht zu polarisieren. Hierzu wird ein sogenanntes \textit{Nicol}-Prisma \index{Nicol-Prisma} verwendet, bei dem zwei Kalkspat-Prismen so zueinander angeordnet werden, dass der außergewöhnliche Strahl an der Grenzschicht total reflektiert wird, wohingegen der gewöhnliche Strahl hindurchgelangen kann. + \item $\lambda$-4-Blättchen: Hierbei handelt es sich um ein anisotropes Medium, meistens ein einachsiges Material, bei dem die beiden senkrecht zueinander stehenden Polarisationsrichtungen um eine viertel-Wellenlänge zueinander phasenverschoben werden. Das heraustretende Licht ist dann im allgemeinen elliptisch polarisiert. Für den Fall, dass der Winkel zwischen der Polarisationsebene und der beiden Achsen 45$^\circ$ beträgt, erhalten wir zirkulär polarisiertes Licht. + \item Spannungsoptik: Transparente plastische Werkstoffe werden unter + Wirkung äußerer Kräfte doppelbrechend. Die resultierenden farbigen Bilder in einem gekreuzten Polarisator können qualitativ (aber auch quantitativ genutzt werden, um innere Spannungen zu erkennen und so zu optimieren bzw. zu + verstärken, dass eine Konstruktion robuster werden kann. + \end{itemize} \begin{figure} \parbox{0.7\linewidth}{ - \includegraphics[width=1.3\linewidth]{Graphiken/ellipsoid_export.png}} + \includegraphics[width=\linewidth]{Graphiken/ellipsoid_export.png}} \parbox{0.3\linewidth}{ \caption{ \label{fig:doppelbrechung} In einem uniaxialen Medium mit $n_1>n_2=n_3$ (positiver Kristall) diff --git a/v0.1/skript.tex b/v0.1/skript.tex index 6fc5d3f..051f1bd 100644 --- a/v0.1/skript.tex +++ b/v0.1/skript.tex @@ -19,9 +19,9 @@ \usepackage[pdftex,colorlinks,linkcolor=blue,citecolor=blue,backref]{hyperref} \hypersetup{ - pdftitle={Skript Experimentalphysik II WS 2018/19}, + pdftitle={Skript Experimentalphysik II Dieter Horns}, pdfauthor={Prof.Dr. Dieter Horns}, - pdfsubject={Your subject here}, + pdfsubject={Physik, Experimentalphysik, Vorlesung}, pdfkeywords={Physik II, Experimentalphysik}, bookmarksnumbered=true, bookmarksopen=true, -- GitLab