From 0e030f238229abf5b019a262494ec5d27f130f62 Mon Sep 17 00:00:00 2001
From: "lorenzo.zolfanelli93" <lorenzo.zolfanelli93@gmail.com>
Date: Fri, 14 Aug 2020 18:15:37 +0000
Subject: [PATCH] Update on Overleaf.

---
 chapters/1-introduction.tex |   32 +
 images/ev_wave.pdf          |  Bin 0 -> 33043 bytes
 images_src/ev_wave.svg      | 2745 +++++++++++++++++++++++++++++++++++
 main.tex                    |    3 +
 4 files changed, 2780 insertions(+)
 create mode 100644 images/ev_wave.pdf
 create mode 100644 images_src/ev_wave.svg

diff --git a/chapters/1-introduction.tex b/chapters/1-introduction.tex
index d7ededf..be0b3e9 100644
--- a/chapters/1-introduction.tex
+++ b/chapters/1-introduction.tex
@@ -634,4 +634,36 @@ degli spostamenti di una proteina.
 
 \subsection{TIRF}
 
+La microscopia di fluorescenza a riflessione interna totale (TIRF)
+permette di ridurre il rumore dovuto alla fluorescenza fuori fuoco
+sfruttando, per l'eccitazione dei fluorofori, un'onda evanescente
+in grado di penetrare solo le prime centinaia di nanometri del
+campione.
 
+L'onda evanescente viene ottenuta facendo incidere il fascio
+di eccitazione all'interfaccia di separazione tra il vetrino
+coprioggetti e il campione con un angolo maggiore rispetto
+all'angolo critico $\theta_c$ definito dalla \emph{legge di Snell}:
+
+\begin{multline}
+    n_i \sin(\theta_i) = n_t \sin(\theta_t) \\
+    \Rightarrow \sin(\theta_t) = \frac{n_i}{n_t} \sin(\theta_i) \\
+    \Rightarrow \left\lvert
+        \frac{n_i}{n_t} \sin(\theta_i)
+    \right\rvert \leq 1 \\
+    \Rightarrow \theta_i \leq \arcsin\left(\frac{n_t}{n_i}\right)
+    \doteq \theta_c
+\end{multline}
+
+Quando un'onda elettromagnetica passa da un mezzo con un indice
+di rifrazione più grande a uno con indice di rifrazione più piccolo,
+e quindi $\theta_c = \arcsin\left(\sfrac{n_t}{n_i}\right)$
+
+
+
+\begin{figure}[ht]
+    \centering
+    \includegraphics[width=\linewidth]{images/ev_wave.pdf}
+    \caption{Caption}
+    \label{fig:ev_Wave}
+\end{figure}
diff --git a/images/ev_wave.pdf b/images/ev_wave.pdf
new file mode 100644
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new file mode 100644
index 0000000..d1ae4c5
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+             xlink:href="#symbol6727" />
+        </g>
+        <g
+           id="g6790"
+           style="fill:#000000;fill-opacity:1">
+          <use
+             height="100%"
+             width="100%"
+             id="use9267"
+             y="81.962997"
+             x="117.259"
+             xlink:href="#symbol5917" />
+        </g>
+        <g
+           id="g7167"
+           style="fill:#000000;fill-opacity:1">
+          <use
+             height="100%"
+             width="100%"
+             id="use4794"
+             y="81.962997"
+             x="116.152"
+             xlink:href="#symbol671" />
+        </g>
+        <g
+           id="g1942"
+           style="fill:#000000;fill-opacity:1">
+          <use
+             height="100%"
+             width="100%"
+             id="use7404"
+             y="81.962997"
+             x="125.561"
+             xlink:href="#symbol4987" />
+        </g>
+      </g>
+    </g>
+  </g>
+</svg>
diff --git a/main.tex b/main.tex
index 3682e98..19cbe75 100644
--- a/main.tex
+++ b/main.tex
@@ -21,6 +21,9 @@
 \usepackage{graphicx}
 \graphicspath{ {images/} }
 
+% ===== MATHS
+\usepackage{amsmath}
+
 % ===== TABLES
 \usepackage{booktabs}
 \usepackage{rotating}