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\begin{document}

\Prova{1}{26 de mar\c{c}o  de 2015}

%\hrulefill

%\vspace{2mm}

\begin{QstsFig}\ (4.0) 

\begin{itemize}
\item{(1.0)}  a) 
\item{(1.0)}  b) 
\item{(0.5)}  c) 
\item{(0.5)}  d) 
\item{(1.0)}  e) 

\end{itemize}
\end{QstsFig}

\newpage

\begin{QstsFig}\ (3.0) 

\begin{itemize}
\item{(1.0)}  a) 
\item{(1.0)}  b) 
\item{(0.5)}  c) 
\item{(0.5)}  d) 
\item{(1.0)}  e) 

\end{itemize}

\end{QstsFig}

\newpage

\begin{QstsFig}\ (3.0) 

\begin{itemize}
\item{(1.0)}  a)
\item{(1.0)}  b) 
\item{(1.0)}  c) 
\item{(0.5)}  d) a dist\^{a}ncia entre o m\'{a}ximo de segunda ordem e o m\'{a}ximo central.
\end{itemize}
\end{QstsFig}


\newpage


Formul\'{a}rio

\vspace{10mm}

\noindent  $\vec  {D}\,=\,\epsilon _{o}\,\vec  {E}\,+\,\vec  {P} $ \ \ \ \ \ \ \ \
$\vec  {B}\,=\,\mu _{o}\,{\,\vec  {H}\,+\,\vec  {M}}$ \ \ \ \ \ \ \ \
$\vec  {D}\,=\,\epsilon \,\vec {E} $ \ \ \ \ \ \ \ \
$\vec  {B}\,=\,\mu \,\vec {H} $

\vspace{3mm}

\noindent  $\nabla .\vec {D}\,=\,\rho $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
$\nabla \times \,\vec  {H}\,=\,\vec {J}\,+\,\frac {\partial \vec {D}}{\partial  t}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
\sigma _{p}\,=\,\vec {P}.\vec {n} $

\vspace{3mm}

\noindent  $\nabla .{\vec {D}}\,=\,\frac {\partial D_{x}}{\partial  x}\,+\,\frac {\partial D_{y}}{\partial y}\,
+\,\frac  {\partial D_{z}}{\partial z}$

\vspace{3mm}

\noindent  $\nabla .{\vec {D}}\,=\,\frac {1}{r}\frac {\partial }{\partial  r}(rD_{r})\,+\,
\frac {1}{r}\frac {\partial D_{\phi}}{\partial \phi}\,
+\,\frac {\partial D_{z}}{\partial z}$ (coord. cil\'{\i}ndricas)

\vspace{3mm}

\noindent  $\nabla {\vec {D}}\,=\,\frac {1}{r^2}\frac {\partial }{\partial  r}(r^2D_{r})\,+\,
\frac {1}{rsen\theta }\frac {\partial}{\partial \theta }(sen\theta D_{\theta })\,
+\,\frac {1}{rsen\theta }\frac {\partial D_{\phi }}{\partial \phi }$


\vspace{3mm}

\noindent  $\nabla  \times \vec {H}\,=\,(\frac {\partial  H_{z}}{\partial  y}\, - \,\frac {\partial H_{y}}{\partial  z})\vec {i}\,+ \,(
\frac {\partial H_{x}}{\partial  z}\, -\,\frac {\partial H_{z}}{\partial  x})\,\vec {j}\,+
 \,(\frac {\partial H_{y}}{\partial  x}\,- \,\frac {\partial H_{x}}{\partial  y})\,\vec {k} $

\vspace{3mm}

\noindent  $\nabla  \times \vec {H}\,=\,(\frac {1}{r}\frac {\partial  H_{z}}{\partial  \phi }\, - \,\frac {\partial H_{\phi }}{\partial  z})\vec {a}_{r}\,+ 
\,(\frac {\partial H_{r}}{\partial  z}\, -\,\frac {\partial H_{z}}{\partial  r})\,\vec {a}_{\phi}\,+
\frac {1}{r} \,(\frac {\partial {(rH_{\phi }})}{\partial  r}\,-\,\frac {\partial H_{r}}{\partial  \phi })\,\vec {a}_{z} $ (coord. cil\'{\i}ndricas)


\vspace{3mm}


$\vec {k}\,\times \,\vec {E}\,=\,\omega \vec {B}
\ \ \ \ \ \ \ \ \ \ \ \ \  \vec {S}\,=\,\frac {1}{\mu }\,\vec {E}\,\times \,\vec {B}
\ \ \ \ \ \ \ \ \ \ \ \ \  P\,=\,f_{a}\,\frac {<S>}{c}\,+\,2f_{r}\,\frac {<S>}{c}\ \ \ \ \ \ \ \ \ \ \ \ \ E_{o}\,=\,cB_{o} $

\vspace{3mm}

$ <p>\,=\,f_{a}\,\frac  {<U>}{c} \,+\,2\,f_{r}\,\frac  {<U>}{c} \ \ \ \ \ \ \ \ \ \ \ \ \  P_{ot}\,=\, \int \vec {S}.\vec {dA}
\ \ \ \ \ \ \ \ \ \ \ \ \  I\,=\,I_{o}\,cos^{2}\,\theta \ \ \ \ \ \ \ \ \    c\,=\,3\times 10^{8}\,m/s$


\vspace{3mm}

$ D_{1n}\,=\,D_{2n} \ \ \ \ \ \ E_{1t}\,=\,E_{2t} \ \ \ \ \ \ B_{1n }\,=\,B_{2n}  \ \ \ \ \ \ H_{1t}\,=\,H_{2t}  \ \ \ \ \ \  \tan \theta _{i}_{B}\,=\,\frac {n_{t}}{n_{i}} \ \ \ \ \ \ 
\theta _{i}\,+\,\theta _{t}\,=\,\frac {\pi }{2}$

\vspace{4mm}

Interfer\^{e}ncia

\vspace{3mm}

$m\lambda \,=\,d\,sen\vspace{1mm}\,\theta  \ \ \ \ \ \ \  (m\,+\,\frac{1}{2})\lambda \,=\,d\,sen\,\theta \ \ \ \ \ \ \ \ $m\lambda \,=\,a\,sen\,\theta $ \ \ \ \ \ \ \  
$(m\,+\,\frac{1}{2})\lambda \,=\,a\,sen\,\theta  $ \ \ \ \ \ \ \  $sen\,\theta\,=\,1.22\,\frac {\lambda }{a}$ 

\lambda _{n}\,=\,\frac {\lambda }{n}$ 

\vspace{3mm}

$m\lambda \,=\,a\,sen\,\theta $ \ \ \ \ \ \ \  $(m\,+\,\frac{1}{2})\lambda \,=\,a\,sen\,\theta  $ \ \ \ \ \ \ \  $sen\,\theta\,=\,1.22\,\frac {\lambda }{a}$

\vspace{3mm}

$I\,=\,I_{o}\,(\frac {sen\,\frac {\beta }{2}}{\frac{\beta }{2}})^{2}\,\,\,(\frac {sen \,\frac {N\phi}{2}}{sen \,\frac{\phi }{2}})^{2} \ \ \ \ \ \ \  
 \phi \,=\,{\frac  {2\pi }{\lambda }{\,d\,sen \,\theta } \ \ \ \ \ \ \ \beta \,=\,{\frac  {2\pi }{\lambda }{\,a\,sen \,\theta } $ \ \ \ \ \ \ \ 
$R\,=\,\frac {\lambda _{m} }{\lambda _{2}\,-\,\lambda _{1}}\,=\,\frac {\lambda _{m}}{\Delta \lambda } \ \ \ \ \ \ \   R\,=\,m\,N $

\vspace{4mm}

Pel\'{\i}cula

\vspace{3mm}

$2nt\,=\,(m\,+\,\frac {1}{2})\,\lambda  \ \ \ \ \ \ \ \ \ \ \ m\,=\,0, 1, 2, ...... $

\vspace{3mm}

$2nt\,=\,m\,\lambda \ \ \ \ \ \ \ \ \ \ \ m\,=\,0, 1, 2, ......$


\vspace{3mm}

$t\,cos\theta _{t}\,=\,(2m\,+\,1)\frac {\lambda _{t}}{4} \ \ \ \ \ \ \ \ \ \ \ m\,=\,0, 1, 2, ......$

\vspace{3mm}

$t\,cos\theta _{t}\,=\,m\,\frac {\lambda _{t}}{2} \ \ \ \ \ \ \ \ \ \ \ m\,=\,0, 1, 2, ......$

\vspace{4mm}

Difra\c{c}\~{a}o

\vspace{3mm}

$sen\,\theta\,=\,1.22\,\frac {\lambda }{a}$

\vspace{3mm}

$m\lambda \,=\,a\,sen\,\theta $

\vspace{3mm}

$(m\,+\,\frac{1}{2})\lambda \,=\,a\,sen\,\theta  $

\vspace{4mm}

$I\,=\,I_{o}\, (\frac {sen\,\frac {\pi a\,sen\,\theta }{\lambda }}{ \frac {\pi a\,sen\,\theta }{\lambda }})^{2}        $

\vspace{4mm}

R\^{e}de de difra\c{c}\~{a}o

\vspace{4mm}

$ m\lambda \,=\,d\,sen\,\theta \ \ \ \ \ \ \ \ \ \ \ \ (m\,+\,\frac{1}{2})\lambda \,=\,d\,sen\,\theta  $

\vspace{4mm}

$I\,=\,I_{o}\, cos^{2}\,(\frac  {\pi d\,sen\,\theta }{\lambda })(\frac {sen\,\frac {\pi a\,sen\,\theta }{\lambda }}{ \frac {\pi a\,sen\,\theta }{\lambda }})^{2} $

\vspace{4mm}

$R\,=\,\frac {\lambda _{m} }{\lambda _{2}\,-\,\lambda _{1}}\,=\,\frac {\lambda _{m}}{\Delta \lambda } \ \ \ \ \ \ \ \ \ \ \ \  R\,=\,m\,N $


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