\(\(Odraznost\ a\ propustnost\ rozhraní\)\(
\)\)
\(\(Rozhraní\ dvou\ homogenních\ izotropních\ dielektrik\)\(
\)\)
\(Přechod\ elektromagnetických\ vln\ z\ prostředí\ řidšího\ do\ hustšího\ \((n\_1 < n\_2)\)\)

\(V\ každé\ úloze\ předpokládáme, \ že\ první\ prostředí\ je\ vzduch\ \((n\_1 = 1)\)\ a\ druhé\ prostředí\ je\ sklo, \ 
      jehož\ index\ lomu\ \(n\_2\) se\ mění\)
\(\(od\ výchozí\ hodnoty\ 1.4\ do\ 1.96\ \ \((rozsah\ indexů\ lomu\ obvyklých\ optických\ skel)\) . \ 
          Animace\ pro\ změnu\ indexů\ lomu\ n\_2\ spustíme\ dvojklikem\)\(\ \)\)
\(\(na\)\(\ \)\(příslušný\)\(\ \)\(graf\)\(\ \ \)\)

\(Koeficient\ odraznosti\ rozhraní\ v\ rovině\ \(dopadu : \ \(r\^ // \)\) = \(-\(\(tg \((α\_1 - α\_2)\)\)\/\(tg \((α\_1 + α\_2)\)\)\)\), \ 
        kde\ α\_1, \ α\_2\ jsou\ úhly\ dopadu\ a\ lomu

        V\ animaci\ je\ patrný\ vzrůst\ hodnoty\ Brewsterova\ úhlu\ při\ zvyšování\ hodnoty\ indexu\ lomu\ n\_2

        \)

n1 = 1;
\(\(r1 = 
        Table[
Plot[
\(-Tan[
                  a1 - ArcSin[n1*Sin[a1]/n2]]\)/
              Tan[a1 + ArcSin[n1*Sin[a1]/n2]], 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(r^ ∥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {\(-0.4\), 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

\(\(Export["n1_mensi_n2_koef_odraznosti_rozhrani_v_rovine_dopadu.gif", \ r1, \ "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];\)\)

\(Koeficient\ odraznosti\ v\ rovině\ kolmé\ k\ rovině\ \(dopadu : \ \(r\^ ⊥ \)\) = \(-\(\(sin \((α\_1 - α\_2)\)\)\/\(sin \((α\_1 + α\_2)\)\)\)\)\)

n1 = 1;
\(\(r2 = 
        Table[
Plot[
\(-Sin[
                  a1 - ArcSin[n1*Sin[a1]/n2]]\)/
              Sin[a1 + ArcSin[n1*Sin[a1]/n2]], 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(r^ ⊥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {\(-1\), 
                0}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_koef_odraznosti_rozhrani_v_rovine_kolme_k_\
rovine_dopadu.gif",  r2,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(\(Koeficient\ propustnosti\ v\ rovině\ \(dopadu : \ \(t\^ ∥ \)\) = \(2\ sinα\_2\ cosα\_1\)\/\(sin \((α\_1 + α\_2)\)\ cos \((α\_1 + α\_2)\)\)\)\(
\)
        \)

n1 = 1;
\(\(t1 = 
        Table[
Plot[
2*
              Sin[ArcSin[n1*Sin[a1]/n2]]*
              Cos[a1]/\((Sin[a1 + ArcSin[n1*Sin[a1]/n2]]*
                    Cos[a1 - 
                        ArcSin[n1*Sin[a1]/n2]])\), 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(t^ ∥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_koef_propustnosti_rozhrani_v_rovine_dopadu.gif\
",  t1,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(\(Koeficient\ propustnosti\ v\ rovině\ kolmé\ k\ rovině\ \(dopadu : \ \(t\^ ⊥ \)\) = \(2\ sinα\_2\ cosα\_1\)\/\(sin \((α\_1 + α\_2)\)\)\)\(
\)
        \)

n1 = 1;
\(\(t2 = 
        Table[
Plot[
2*
              Sin[ArcSin[n1*Sin[a1]/n2]]*
              Cos[a1]/Sin[
                  a1 + ArcSin[n1*Sin[a1]/n2]], 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(t^ ⊥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_koef_propustnosti_rozhrani_v_rovine_kolme_k_\
rovine_dopadu.gif",  t2,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(Odraznost\ rozhraní\ v\ rovině\ \(dopadu : \ \(R\^ ∥ \)\) = \((\(r\^ ∥ \))\)\^2\)

n1 = 1;
\(\(RR1 = 
        Table[
Plot[
\((\(-Tan[
                      a1 - ArcSin[n1*Sin[a1]/n2]]\)/
                  Tan[a1 + 
                      ArcSin[n1*Sin[a1]/n2]])\)^2, 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(R^ ∥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_odraznost_rozhrani_v_rovine_dopadu.gif",  
        RR1,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(Odraznost\ rozhraní\ v\ rovině\ kolmé\ k\ rovině\ \(dopadu : \ \(R\^ ⊥ \)\) = \((\(r\^ ⊥ \))\)\^2\)

n1 = 1;
\(\(RR2 = 
        Table[
Plot[
\((\(-Sin[
                      a1 - ArcSin[n1*Sin[a1]/n2]]\)/
                  Sin[a1 + 
                      ArcSin[n1*Sin[a1]/n2]])\)^2, 
{a1, 0, 
              Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(R^ ⊥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_odraznost_rozhrani_v_rovine_kolme_k_rovine_\
dopadu.gif",  RR2,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(Propustnost\ rozhraní\ v\ rovině\ \(dopadu : \ \(T\^ ∥ \)\)\)=(((Subscript[n, 2]) cos(Subscript[α, 2]))/((Subscript[n, 1]) cos(Subscript[α, 1])))((((t^ ∥) ))^2);   \(\(T\^ ∥ \) + \(R\^ ∥ \) = 1. \)

n1 = 1;
\(\(TT1 = 
        Table[
Plot[
1 - \((\(-Tan[
                        a1 - ArcSin[n1*Sin[a1]/n2]]\)/
                    Tan[a1 + 
                        ArcSin[n1*Sin[a1]/n2]])\)^2, 
{a1, 
              0, Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(T^ ∥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_propustnost_rozhrani_v_rovine_dopadu.gif",  
        TT1,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];

\(Propustnost\ rozhraní\ v\ rovině\ kolmé\ k\ rovině\ \(dopadu : \ \(T\^ ⊥ \)\)\)=(((Subscript[n, 2]) cos(Subscript[α, 2]))/((Subscript[n, 1]) cos(Subscript[α, 1])))((((t^ ⊥) ))^2);   (T^ ⊥)  + (R^ ⊥)  = 1.

n1 = 1;
\(\(TT2 = 
        Table[
Plot[
1 - \((\(-Sin[
                        a1 - ArcSin[n1*Sin[a1]/n2]]\)/
                    Sin[a1 + 
                        ArcSin[n1*Sin[a1]/n2]])\)^2, 
{a1, 
              0, Pi/2}, 
AxesLabel -> {
StyleForm[\*""(Subscript[α, 1])"", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"], 
StyleForm[\*""(T^ ⊥) "", 
                  FontFamily -> "Times", FontSize -> 16, 
                  FontWeight -> "Bold"]
}, 
PlotStyle -> {Thickness[ .008]}, 
Ticks -> {{{Pi/
                      2, \ \*""(π/2)""}, {ArcTan[n2/n1], 
                    ArcTan[n2/n1]}}, 
                Automatic}, 
PlotRange -> {0, 
                1}
], 
{n2, 1.4, 1.96, 
            0.02}
];\)\)

Export["n1_mensi_n2_propustnost_rozhrani_v_rovine_kolme_k_rovine_\
dopadu.gif",  TT2,  "GIF", ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];