Light Reflection and Optical Properties of a Parabola
2019-03-06 06:28
This GeoGebra applet dynamically demonstrates the optical reflection properties of a parabola. Users can interactively adjust the initial emission point P_0 and the first reflection point I_0 on the parabola to observe the changing path of the reflected light rays. Combining geometric and algebraic objects such as parabolas, vectors, lines, and sequences, the model visually illustrates the focal r
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Conic Sections | GeoGebra Book Collection
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<layer val="1"/>
<labelMode val="0"/>
<font serif="true" sizeM="1" size="0" style="1"/>
<absoluteScreenLocation x="41" y="28"/>
</element>
<expression label="text6" exp=""可調整P_0和I_0之位置""/>
<element type="text" label="text6">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<absoluteScreenLocation x="33" y="431"/>
</element>
<expression label="F_1" exp="F" type="point" />
<element type="point" label="F_1">
<show object="true" label="false" ev="8"/>
<condition showObject="¬PAR"/>
<objColor r="175" g="238" b="238" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="5" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="II">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="boolean" label="F1">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<condition showObject="FF ≠ 0"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="26" y="263"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(FF,If(F1,SetValue[PARA,false],SetValue[PARA,true]),SetValue[F1,false])
If(F1,SetValue[I_0,Intersect(Ray(P_0+0.001*Vector(P_0, F_1), F_1), c)])
If(F1,StartAnimation[t,false])
If(F1,SetValue[i,1])
If(F1,SetValue[t,0])
If(start&&F1,SetValue[kk,k])
If(start&&F1,StartAnimation[t,true])"/>
<caption val="通過焦點"/>
</element>
<element type="boolean" label="PARA">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="FF ≠ 0"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="25" y="295"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(FF,If(PARA,SetValue[F1,false],SetValue[F1,true]),SetValue[PARA,false])
If(PARA,SetValue[I_0,Intersect(OrthogonalLine(P_0, f), c)])
If(PARA,StartAnimation[t,false])
If(PARA,SetValue[i,1])
If(PARA,SetValue[t,0])
If(start&&PARA,SetValue[kk,k])
If(start&&PARA,StartAnimation[t,true])"/>
<caption val="平行對稱軸"/>
</element>
<expression label="a" exp="Length[S_I] - If[II ≟ II, 0, 1]" />
<element type="numeric" label="a">
<value val="0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="If">
<input a0="II ≟ II" a1="1" a2="-1"/>
<output a0="testa"/>
</command>
<element type="numeric" label="testa">
<value val="-1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
</construction>
</geogebra>