From a72a1cb9a324b7d39b47d83f99e2cd79dc3a94c5 Mon Sep 17 00:00:00 2001
From: Filip Znachor <filip@znachor.cz>
Date: Mon, 12 Jun 2023 14:13:26 +0200
Subject: [PATCH] =?UTF-8?q?P=C5=99id=C3=A1n=C3=AD=2011.=20p=C5=99=C3=ADkla?=
 =?UTF-8?q?du=20z=20FYI?=
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---
 KFY FYI1/Priklad11.md          | 25 +++++++++++++++++++++++++
 KFY FYI1/_assets/priklad11.svg |  4 ++++
 2 files changed, 29 insertions(+)
 create mode 100644 KFY FYI1/Priklad11.md
 create mode 100644 KFY FYI1/_assets/priklad11.svg

diff --git a/KFY FYI1/Priklad11.md b/KFY FYI1/Priklad11.md
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+++ b/KFY FYI1/Priklad11.md	
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+### Zadání
+
+Paprsek bílého světla dopadá ve vzduchu na flintové sklo (druh skla používaného v optice) pod úhlem 60°. Index lomu flintového skla pro červené světlo vlnové délky 761 nm je 1,735 a pro fialové světlo vlnové délky 397 nm je 1,811. Určete úhel mezi lomeným červeným a fialovým paprskem.
+
+- $\alpha = 60^\circ$
+- $v_{č} = 1.735$
+- $v_{f} = 1.811$
+- $\gamma = ?$
+
+![](_assets/priklad11.svg)
+
+z obrázku vidíme, že $\gamma = \beta_{č} - \beta_{f}$
+
+pro stanovení úhlu lomu $\beta$ využijeme Snellův zákon
+- pro **červený paprsek** dostaneme
+	- $\displaystyle \frac{\sin \alpha}{\sin \beta_{č}} = \frac{v_{č}}{v_{v}} = v_{č} \qquad (v_{v} \sim 1)$
+	- vyjádříme $\displaystyle \sin \beta_{č} = \frac{\sin \alpha}{v_{č}}$
++ pro **fialový paprsek** dostaneme
+	+ $\displaystyle \frac{\sin \alpha}{\sin \beta_{f}} = \frac{v_{f}}{v_{v}} = v_{f}  \qquad (v_{v} \sim 1)$
+	+ vyjádříme $\displaystyle \sin \beta_{f} = \frac{\sin \alpha}{u_{f}}$
+
+vypočítáme výsledný úhel
+- $\displaystyle \gamma = \beta_{č} - \beta_{f} = \arcsin\left(\frac{\sin \alpha}{u_{č}}\right) - \arcsin\left( \frac{\sin \alpha}{u_{f}} \right)$
+- dosadíme
+	- $\gamma = \arcsin\left( \frac{\sin 60^\circ}{1.735} \right) - \arcsin\left( \frac{\sin 60^\circ}{1.811} \right) = 1.375692^\circ$
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diff --git a/KFY FYI1/_assets/priklad11.svg b/KFY FYI1/_assets/priklad11.svg
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