Pst Optic Doc

8/16/2019 Pst Optic Doc

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PSTricks

pst-optic

Lenses and Mirrors; v.1.01

July 23, 2010

Documentation by Package author(s):Herbert Voß Manuel Luque

Herbert Voß


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Contents 2

Contents

1 General Options 51.1 \resetOpticOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Optical axis line style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Lenses 72.1 The Coordinates of the predened Nodes . . . . . . . . . . . . . . . . . . . . 72.2 The Lens Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 \Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 \rayInterLens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 \telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Mirrors 133.1 options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 \mirrorCVG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 \mirrorDVG 164.1 Drawing Rays in the Mirror Macros . . . . . . . . . . . . . . . . . . . . . . . 174.2 \planMirrorRay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.3 \symPlan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.4 Beam Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Refraction 20

6 \refractionRay 206.1 Total Reection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7 Prism 217.1 Figure with default values and construction indications . . . . . . . . . . . . 227.2 Figure with default values, without construction indications . . . . . . . . . 227.3 Color matches wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8 Spherical Optic 258.1 \lensSPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9 \mirrorCVG 27

10 \mirrorDVG 27

11 \ABinterSPHLens 28

12 \lensSPHRay 28

13 \reflectionRay 3113.1Refraction at a Spherical surface . . . . . . . . . . . . . . . . . . . . . . . . . 32


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Contents 3

14Utility Macros 3314.1 \eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

15 \Arrows 34

16 \psOutLine and \psBeforeLine 34

17 \Parallel 35

18 \ABinterCD and \nodeBetween 35

19 \rotateNode 36

20 \rotateTriangle 36

21 \rotateFrame 37

22 \arrowLine 38

22.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3823List of all optional arguments for pst-optic 40

References 41


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pst-optic loads by default the following packages: pstricks , pst-node , pst-plot ,pst-3d , pst-grad , pst-math , multido , and pst-xke . All should be already part of yourlocal T EX installation. If not, or in case of having older versions, go to http://www.CTAN.org/ and load the newest version.

Thanks to: Jean-Côme Charpentier, Arnaud Schmittbuhl.

http://www.ctan.org/http://www.ctan.org/http://www.ctan.org/http://www.ctan.org/


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1.1 \resetOpticOptions 6

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-2

-1

0

1

2

3

4

A

B

A′

B ′

O

1 \ begin {pspicture}[showgrid=true](-5,-2.2)(7,4)2 \ rput (1.5,1.5){ %3 \ lens [lensType=DVG,lensGlass=true,lensWidth=0.5,rayColor=red,4 focus=-2,AB=2,spotAi=270,spotBi=90]}5 \ end {pspicture}

1.1 \resetOpticOptions

The Macro \resetOpticOptions resets all pst-optic options to the default value.

1.2 Optical axis line style

pst-optic denies a line style opticalAxis with the predenes values of:

\ newpsstyle {opticalAxis}{linewidth=0.5pt,linecolor=black,linestyle=solid}

It can be overwritten in the same way with \newpsstyle .

|

F ′|

FA

B

A ′

B ′

O

1 \ newpsstyle {opticalAxis}{linewidth=0.5pt,linecolor=blue,linestyle=dashed}2 \ lens


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2.3 \Transform 9

Using \lens [lensType=...] gives the in gures 2 and 4 shown lenses with the de-fault values from Table 2 .

Table 2: Available options for lenses with the defaults

Option Name Default Lense type ( CVG| DVG| PCVG|PDVG) lensType CVGLense height in cm lensHeight 5cmLense width in cm lensWidth 0.5cm 1

vertical scale (obsolet) lensScale 1 View the lens lensGlass falseSecond lens lensTwo falseFocus in cm focus 2Distance OA OA -4Distance AB AB 1.5Lens color lenscolor Arrow length in cm lensarrowsize 0.2 Arrow inset in cm lensarrowinset 0.5

1 only for lensGlass=true , otherwise set to 2\pslinewidth

The origin of the coordinate system is by default vertically and horinzontally sym-metric. If you want to place the lens at another coordinates then dene your ownpspicture -environment and use the \rput -command:

\ begin {pspicture}(-7.5,-3)(7.5,3)\ rput (x,y){\ lens [...]}

\ begin {pspicture}\ begin {pspicture *}(-7.5,-3)(7.5,3)

\ rput (x,y){\ lens [...]}\ begin {pspicture *}

The star version enables the clipping option.

2.3 \Transform

The \Transform -macro renames all existing nodes in names with an additional „1“.Table 3 shows a list of all nodes. \Transform also denes a new node factice withthe coordinates (XO1,YO1) . The renaming of all nodes makes it easier to handle objectswith more than one lens. With the option lensTwo=true it is possible to chain the

different rays of the lenses (Figure 8).

Table 3: Renaming of the nodes after calling the macro \Transform

old A B A’ B’ O F F’ I I’ XO YO OA’ A’B’new A1 B1 A’1 B’1 O1 F1 F’1 I1 I’1 XO1 YO1 O1A1’ A’1B’1


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2.3 \Transform 10

|

F ′|

FA

B

A ′

B ′

O|

F ′|

FA

B

O

1 \ begin {pspicture *}(-7.5,-2.75)(7.5,3)2 \ rput (0,0){\ lens [lensScale=0.6,XO=-4,focus=1, OA=-2,lensGlass=true, lensWidth=0.5]}3 \ rput (0,0){\ lens [lensScale=1.2,XO=2,focus=2,lensGlass=true,lensWidth=0.5]}4 \ end {pspicture *}

Figure 6: Denition of two unchained lenses

|

F ′|

FA

B

A ′

B ′

O|

F ′|

FAB

A ′B ′

O

1 \ begin {pspicture *}(-7.5,-2.75)(7.5,3)2 \ rput (0,0){\ lens [lensScale=0.6,XO=-4,focus=1, OA=-2,lensGlass=, lensWidth=0.5]}3 \ Transform4 \ rput (0,0){\ lens [lensScale=1.2,XO=2,focus=2,lensTwo=true,lensGlass=true,lensWidth=0.5]}5 \ end {pspicture *}

Figure 7: Denition of two chained lenses


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2.3 \Transform 11

|

F ′1|

F 1A 1

B 1

O 1|

F ′2|

F 2

A ′1

B ′1

A ′2

B ′2

O 2

1 \ begin {pspicture *}(-7.5,-2.75)(7.5,3)2 \ rput (0,0){\ lens [lensScale=0.6,XO=-4,nameF=F _1,nameA=A _1,nameB=B _1,3 nameFi=F’ _1,nameAi={ },nameBi={},nameO=O _1,focus=1, OA=-2,lensGlass=true, lensWidth

=0.5]}4 \ pspolygon [style=rayuresJaunes,linestyle=none](B)(I)(B’)(I’)(B)5 \ Transform6 \ rput (0,0){\ lens [lensScale=1.2,XO=2,focus=2,nameA=A’ _1,spotA=90,nameB=B’ _1,spotB=270,7 nameO=O_2,nameAi=A’ _2,spotAi=270,nameBi=B’ _2,spotBi=90,nameF=F _2,nameFi=F’ _2,8 lensTwo=true,lensGlass=true,lensWidth=0.5]}9 \ pspolygon [style=rayuresJaunes,linestyle=none](B)(I)(B’)(I’)(B)

10 \ end {pspicture *}

Figure 8: Denition of two chained lenses and an additional modication of the node la-bels.


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2.4 \rayInterLens 12

2.4 \rayInterLens

This macro is only useful for a two-lens-system. Figure 9 shows such a system. Thenodes B1, I11 , F’1 , and B’1 are predened by the \lens -macro. To draw the two raysfrom the left lense via the node B’1 to the second lens, we need the coordinates of thesepoints. \rayInterLense denes such nodes. The Syntax:

\rayInterLense( StartNode )( IntermediatNode )( LensDistance ){ LensNode }

Two parallel lines are drawn with the \Parallel -Macro.

B1O

O1

I11

B ′1

Inter1L2

1 \ begin {pspicture *}(-7.5,-4)(7.5,4)2 \ rput (0,0){\ lens [focus=1.5, OA=-2,AB=0.6,XO=-5,lensGlass,yBottom=-4,yTop=4,drawing=false,3 lensWidth=0.5,lensScale=0.5,nameF=F _1,nameFi=F’ _1]}4 \ psline [linewidth=1pt](xLeft)(xRight)5 \ Transform6 \ rput (0,0){\ lens [focus=2,XO=4,lensGlass,yBottom=-4,yTop=4,drawing=false,lensWidth=0.5,7 lensHeight=7,nameF=F _2,nameFi=F’ _2,spotF=90,spotFi=90]}8 \ psline {->}(A1)(B1)\ psline {->}(A’1)(B’1)9 \ psset {linecolor=red}

10 \ uput [45](B1){B1} \ uput [90](O){O} \ uput [225](O1){O1} \ uput [45](I11){I11} \ uput [45](B’1){$B’ _1$}

11 \rayInterLens(I11)(B’1){4}{Inter1L2} \rayInterLens(O1)(B’1){4}{Inter2L2}12 \ uput [350](Inter1L2){Inter1L2}

13 \ psline (B1)(I11)(B’1)(Inter1L2) \ psline (B1)(O1)(B’1)(Inter2L2)14 \Parallel(B’1)(O)(Inter2L2){B2inftyRigth} \Parallel(B’1)(O)(Inter1L2){B3inftyRigth}15 \ psset {length=-2,linestyle=dashed}16 \Parallel(B’1)(O)(Inter2L2){B2inftyLeft} \Parallel(B’1)(O)(Inter1L2){B3inftyLeft}17 \ psline [linestyle=dotted, linewidth=2pt,linecolor=black]{->}(0,-4)(0,+4)18 \ end {pspicture *}

Figure 9: Demonstration of \rayInterLens


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2.5 \telescope 13

2.5 \telescope

Figure 10 shows the conguration of a telescope and Table 4 the special options for the\telescop -Macro.

F 1

F 2

1 \telescope

Figure 10: \telescope -Macro

3 Mirrors

3.1 options

Figure 11 shows the available mirrors and Table 4 the possible options.

1

2

− 1

− 2

−

1 21

Focus

m i r r o r H e

i g h t

mirrorDep

mirrorWid

mirrorColo

1 \ begin {pspicture *}[showgrid=true](-1,-3)(3,3)2 \ rput (0,0){\mirrorCVG[mirrorColor=gray,drawing=false]}3 \ psaxes [linestyle=dashed,linecolor=red,linewidth=1pt, arrows

=->](0,0)(-1,-3)(3,3)4 \ qdisk (Focus){2pt} \ rput (Focus){\ rput (0,0.25){Focus}}5 \ pcline [ arrows =|-|](-0.75,-2.5)(-0.75,2.5)\ ncput *[nrot=:U]{

mirrorHeight}6 \ pcline [ arrows =|-|](0,2.75)(1,2.75) \ rput [l](1.1,2.75){

mirrorDepth}7 \ pcline [ arrows =|-|](1,-2.75)(0.75,-2.75) \ rput [l](1.1,-2.75){

mirrorWidth}8 \ rput [l](1,-1){mirrorColor}9 \ psline {


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3.1 options 14

Table 4: List of options for mirrors with the predenes values

Option Name Default Left value of the picture in cm xLeft -0.5Right value of the picture in cm xRight 11

Lowest value of the picture in cm xBottom -6Highest value of the picture in cm xTop 2.5Mirror height in cm mirrorHeight 5Mirror depth in cm mirrorDepth 1Mirror width in cm mirrorWidth 0.25Mirror color mirrorColor lightgrayRay color rayColor black Focus in cm (only together with the optionposMirrorTwo senseful)

mirrorFocus 8

Position of the 2. mirror in cm posMirrorTwo 8Inclination of the 2. mirror in degrees mirrorTwoAngle 45

Draw lines drawing true

1

2

− 1

− 2

−

− 1− 2− 34 m

i r r o r H e

i g h t

mirrorDepth

mirrorWidth

irrorColor

1 \ begin {pspicture *}[showgrid=true](-4,-3)(1,3)2 \ rput (0,0){\mirrorDVG[mirrorColor=gray,drawing=false]}3 \ psaxes [linestyle=dashed,linecolor=red,linewidth=1pt,

arrows =->](0,0)(-4,-3)(1,3)4 \ qdisk (Focus){2pt} \ rput (Focus){\ rput

(0,0.25){Focus}}5 \ pcline [ arrows =|-|](.5,-2.5)(.5,2.5) \ ncput *[nrot=:U]{

mirrorHeight}6 \ pcline [ arrows =|-|](-1.25,2.75)(-.25,2.75) \ rput [r

](-1.3,2.75){mirrorDepth}7 \ pcline [ arrows =|-|](-1.25,-2.75)(-1,-2.75) \ rput [r

](-1.3,-2.75){mirrorWidth}8 \ rput [r](-2,-2){mirrorColor} \ psline {->}(-2,-2)

(-0.9,-2)9 \ end {pspicture *}

-2 -1 0 1 2

-2

-1

0

1

2

M 1

M 2 A

A ′

1 \ begin {pspicture}[showgrid=true](-2,-2)(2,2)2 \ pnode (-1.5,-1.5){M1} \ pnode (1,1){M2}3 \ uput [-90](M1){$\mathrm{M _1}$}\ uput [90](M2){$\mathrm{M _2}$}4 \ pnode (-1.5,1.5){A}5 \planMirrorRay(A)(M1)(M2){A’}6 \ psline [linewidth=5pt](M1)(M2)\ pscircle *(A){2pt}7 \ uput [0](A){A} \ uput [0](A’){$\mathrm{A’}$}

8 \ pscircle *(A’){2pt} \ psline [linestyle=dashed](A)(A’)9 \ end {pspicture}

Figure 11: The different mirror macros: a) \mirrorCVG b) \mirrorDVG c) \planMirrorRay


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3.2 \mirrorCVG 15

3.2 \mirrorCVG

Figure 12 shows the default for the \mirrorCVG -macro with the predened nodes anf three default rays.

CenterF A

B

A’

B’

1 \ begin {pspicture *}[showgrid=true](-1,-3)(6,3)2 \ rput (0,0){\mirrorCVG[rayColor=red]}3 \ end {pspicture *}

Figure 12: Parabolic Mirror \mirrorCVG

1 \ begin {pspicture *}(-0.5,-4)(8,4)2 \ rput (0,0){\mirrorCVG[mirrorHeight

=8,mirrorDepth=4,drawing=false

]}3 \ multido {\rY=-4.00+0.25}{33}{ %4 \mirrorCVGRay[linewidth=0.5pt,

mirrorHeight=8,5 mirrorDepth=4](10,\rY)(1,\rY){

Dummy}}6 \ end {pspicture *}

Figure 13: Example


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4 \mirrorDVG 16

4 \mirrorDVG

C F A

BPR

PR’

MR

MR’

FR FR’

1 \ begin {pspicture*

}[showgrid=true](-2,-2.6)(5,3)

2 \ rput (0,0){\mirrorDVG[rayColor=red]}3 \ end {pspicture *}

Figure 14: \mirrorDVG

GG’

1 \ begin {pspicture *}[showgrid=true](-4,-4)(6,4)2 \ rput (0,0){\mirrorCVG[drawing=false,mirrorDepth=0.75,mirrorHeight=7]}3 \ qdisk (Focus){2pt} \ rput (6,2.5){\eye}4 \ pnode (1.75,-1.5){A}\ pnode (1.75,1){B}\ psline [ arrows =->,linewidth=4pt](A)(B)5 \ uput {0.2}[0](2,0){\Huge G} \ psset {linecolor=red}6 \mirrorCVGRay[rayColor=red,mirrorHeight=7,mirrorDepth=0.75](A)(0,-0.9){P1}7 \psOutLine[length=3](P1)(P1’){PEnd}\psBeforeLine[length=5,linestyle=dashed](P1)(P1’){PBegin}8 \mirrorCVGRay[rayColor=red,mirrorHeight=7,mirrorDepth=0.75](A)(0,-0.2){P2}9 \psOutLine[length=3](P2)(P2’’){PEnd}\psBeforeLine[length=5,linestyle=dashed](P2)(P2’){PBegin}

10 %11 \mirrorCVGRay[rayColor=red,mirrorHeight=7,mirrorDepth=0.75](B)(0,2.75){P3}12 \psOutLine[length=3](P3)(P3’){PEnd}\psBeforeLine[length=5,linestyle=dashed](P3)(P3’){PBegin}13 \mirrorCVGRay[rayColor=red,mirrorHeight=7,mirrorDepth=0.75](B)(0,1.8){P4}14 \psOutLine[length=3](P4)(P4’){PEnd}\psBeforeLine[length=5,linestyle=dashed](P4)(P4’){PBegin}15 \ABinterCD(P3)(P3’)(P4)(P4’){A’}\ABinterCD(P1)(P1’)(P2)(P2’){B’}16 \ psline [ arrows =->,linewidth=4pt,linestyle=dashed](B’)(A’)17 \nodeBetween(A’)(B’){G’’}\ uput {0}[0](G’’){\Huge G’}18 \ end {pspicture *}

Figure 15: Example as a magnier


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4.1 Drawing Rays in the Mirror Macros 17

4.1 Drawing Rays in the Mirror Macros

There are two different macros for drawing rays:

\mirrorCVGRay [Options] ( Node1 )( Node2 ){ MirrorNode }\mirrorDVGRay [Options] ( Node1 )( Node2 )( MirrorNode )

The MirrorNode maybe :MirrorNode rst point on the mirrorMirrorNode’ end node or second point on the mirror if one more reection happensMirrorNode” end node for a second reection

If there are only one reection, then MirrorNode’ and MirrorNode” are the same.

4.2 \planMirrorRay

The \planMirrorRay -Macro caculates the coordinates of a mirrored point. In Figure 11is a given node A, whereas A’ is calculated by the macro. The syntax is:

\planMirrorRay( Mirrorbegin )( Mirrorend )( Originalpoint ){ New point }

The macro doesn’t draw any lines, only the coordinates of the new point are saved bythe new node name.

4.3 \symPlan

\symPlan allows to mirroring complete plain graphical objects along a virtual centerline. Figure 16 shows that this mirroring is a mathematical one and not a physical one.For more examples look at [ ? ]. The syntax is:

\symPlan( node1 )( node2 ){ graphic object }

The two nodes dene the mirror axis and the graphics object is in most cases a userdened macro, f.ex: This example needs the package pst-text for the \pstextpathmacro.


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4.3 \symPlan 18

M1

M2

D i e T E X n

i s c h e

K o m ö d ie v o n

D A N T E

D ie TE X n i

s c h

e K o

m ö d i e

v o n D A N T E

1 \newcommand{\dtk}{\ pstextpath (0,0){ %2 \ psplot [linestyle=none]{0}{8}{x sqrt sqrt 2 mul}} %3 {\Large Die \TeX{}nische Kom\"odie von DANTE}}4 \ begin {pspicture}(-4.5,-2.5)(2.5,5)5 \ pnode (-4,-2){M1} \ uput [-90](M1){M1}6 \ pnode (4,4){M2}\ uput [90](M2){M2}7 \ psline [linewidth=5\pslinewidth,linecolor=lightgray](M1)(M2)8 \ rput (-3.5,-1.75){\dtk}9 \symPlan(M1)(M2){\ rput (-3.5,-1.75){\dtk}}

10 \ end {pspicture}

Figure 16: Demonstration of the \symPlan -Macro


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5 Refraction 20

5 Refraction

6 \refractionRay

The syntax is

\refractionRay( A )( B )( C )( D ){ n1 }{ n2 }{ EndNode }

The macro uses the law of Snell

n 1n 2

= sin β sin α

(1)

where the n 1 and n 2 are the refraction numbers with the predened values

n 1 = 1 (2)

n 2 = 1 .41 (3)

and α the incoming abd β the outgoing angle of the ray.The refractionnumbers have the internal names refractA and refractB . A total reection instead of a refraction is possible, when the ray starts in a medium

with a higher refrectionnumber. This happens when sin β > 1 in Equ. 1 . In this case wehave α = β , a total reection.

0 1 2 3 4 5

0

1

2

3

4

5

A

B

C

D

n 1 n 2

E E’

1 \ begin {pspicture}[showgrid=true](5,5)2 \ pnode (0.5,1.5){A}\ qdisk (A){2pt}\ uput [90](A){A}3 \ pnode (2,3){B}\ qdisk (B){2pt}\ uput [90](B){B}4 \ psline [linewidth=1.5pt,linecolor=red]{->}(A)(B)

5 \ pnode (3,5){C}\ qdisk (C){2pt}\ uput [225](C){C}6 \ pnode (4,0){D}\ qdisk (D){2pt}\ uput [135](D){D}7 \ pspolygon [fillstyle=solid,fillcolor=lightgray,8 linecolor=lightgray](C)(D)(5,0)(5,5)(C)9 \ psline [linewidth=1.5pt,linecolor=red](C)(D)

10 \ rput (2,2){\Large$n _1$} \ rput (4.5,2){\Large$n _2$}11 \refractionRay(A)(B)(C)(D){1}{4}{E}12 \ psline [linestyle=dashed,linecolor=red](B)(E)13 \ psline [linestyle=dashed,linecolor=red](E)(E’)14 \ qdisk (E){2pt}\ uput [-20](E){E}15 \ qdisk (E’){2pt}\ uput [-90](E’){E’}16 \ end {pspicture}

The macro needs the values for the four nodes, the two refractionnumbers and thename for the end node. As you can see in the gure the end node of the ray is theintermediate point between the linear ray and the linear medium. The end node of therefracted ray has the same name with an additional single quotation mark. In the gurethe macro was called as

\refractionRay( A )( B )( C )( D ){ 1 }{ 4 }{ E }

n 1 < n 2 (4)


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6.1 Total Reection 21

It is no problem to draw a ray which is going straight through another medium. It canbe done by using the macro twice as shown in the following examples.

6.1 Total Reection

0 1 2 3 4 5

0

1

2

3

4

5

A

B

C

D

n 1 n 2

EE’

1 \ begin {pspicture}[showgrid=true](5,5)

2 \ pnode (0.5,1.5){A}\ pnode (2,3){B}3 \ pnode (3,5){C} \ pnode (4,0){D}4 \ pspolygon [fillstyle=solid,fillcolor=lightgray,5 linecolor=lightgray](C)(D)(0,0)(0,5)(C)6 \ qdisk (A){2pt}\ uput [90](A){A}7 \ qdisk (B){2pt}\ uput [90](B){B}8 \ qdisk (C){2pt}\ uput [225](C){C}9 \ qdisk (D){2pt}\ uput [135](D){D}

10 \ psline [linewidth=1.5pt,linecolor=red]{->}(A)(B)11 \ psline [linewidth=1.5pt,linecolor=red](C)(D)12 \ rput (2,2){\Large$n _1$}\ rput (4.5,2){\Large$n _2$}13 \refractionRay(A)(B)(C)(D){4}{1}{E}14 \ psline [linestyle=dashed,linecolor=red](B)(E)15 \ psline [linestyle=dashed,linecolor=red](E)(E’)16 \ qdisk (E){2pt}\ uput [-20](E){E}17 \ qdisk (E’){2pt}\ uput [-90](E’){E’}18 \ end {pspicture}

In the gure the macro was called as

\refractionRay(A)(B)(C)(D){4}{1}{E}

n 1 > n 2 (5)

7 Prism

This command allows to simulate the deviation of a mono-chromatic light ray with aprism. There are only few parameters. The indicated values are the default ones.name meaning default AnglePrism The angle to the top of prism. 60AnglePlan1 The angle between the plane (1), where the tranmitter takes

place, and the vertical. Negative values are allowed.25

AnglePlan2 The angle between the plane (2) (the screen), and the vertical.

Negative values are allowed.

55

k Position of transmitter relative to choosen origin C 1 on the plane: −−−→C 1 E 1 = k−→u 1 .

1

lambda The wavelength , in nm. 632.8notations The plane where transmitting source takes place, with all indi-

cations, origin, angle, etc., as well as the screen are displayedby default. This can be useful in order to nalize a gure, but itis possible to deactivate this feature with the option.

false


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7.1 Figure with default values and construction indications 22

With AnglePlan1 the incident ray direction can be changed. The incidence spotchanges according to k .

The outline of processing we have adopted is the Gernot Hoffmann one. For more de-tails look into the document: http://www.fho-emden.de/~hoffmann/prism16072005.pdf

7.1 Figure with default values and construction indications

i 1r 1I 1 r 2

i 2I 2

A

D

C 1

E 1C 2

R 2

ρ1

−→u 1

−→n 1ρ2 −→n

−→u 2

1 \ begin {pspicture *}(-8,0)(8,8)2 \psprism


7.2 Figure with default values, without construction indications

i 1r 1I 1 r 2

i 2I 2

A

D

1 \ begin {pspicture *}(-8,0)(8,6)2 \psprism[notations=false]3 \ end {pspicture *}

http://www.fho-emden.de/~hoffmann/prism16072005.pdfhttp://www.fho-emden.de/~hoffmann/prism16072005.pdfhttp://www.fho-emden.de/~hoffmann/prism16072005.pdfhttp://www.fho-emden.de/~hoffmann/prism16072005.pdf


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7.3 Color matches wavelength 23

7.3 Color matches wavelength

i 1r 1I 1 r 2

i 2I 2

A

D

C 1

E 1C 2

R 2

ρ1

−→u 1

−→n 1ρ2 −→

n−→u 2

1 \ begin {pspicture *}(-8,0)(8,8)2 \psprism[lambda=530] %3 \ end {pspicture *}

Note: we have not planned physical impossibilities. When r 2 is greater than the limitangle, there is no transmission in air, and it’s impossible to calculate i2 . Then, we havea PostScript message:

1 Displaying page 12 Displaying page 23 Displaying page 34 Displaying page 45 Error: /rangecheck in --sqrt--6 Operand stack:7 alpha2 -1.02701 -0.0547467

We remind you that alpha2 is i2 .For instance, AnglePrism =65, other default parameters remains unchanged.


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7.3 Color matches wavelength 24

x

i 1r 1I 1 r 2 i 2

I 2

A

D

C 1

1

R 2

ρ1

−→u 1

−→n 1ρ2

−→u 2

1 \ begin {pspicture *}(-7,-0.2)(7,8)2 \psprism[AnglePrism=65]3 \ end {pspicture *}

It will become right when we change the incident ray slope:

x

i 1 r 1I 1

r 2i 2

I 2

A

D

C 1

E 1

C 2

R 2

ρ1

−→u 1 −→n 1

ρ2 −→n

−→u 2

1 \ begin {pspicture *}(-8,-0.2)(8,8)2 \psprism[AnglePrism=65,AnglePlan1=51,k=-1.5]3 \ end {pspicture *}

We choose k=-1.5 in order to have a incident ray which strikes (?) the input sideroudly in its center. But, in these particular cases, the physicist know-how is important(bis repetita ). Isn’t it?


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8 Spherical Optic 25

8 Spherical Optic

8.1 \lensSPH

The syntax is

\lensSPH [Options]

It changes some default values for the options to:

meaning name defaultObject Distance in cm OA -7Lens Height in cm lensHeight 6Lens Width in cm lensWidth 1.5Refraction Number n 2 refractB 2

Convergent Lens

Without any option it draws a spherical convergent lens. \lensSPH is equivilant to\lensSPH[ lensType=CVG ] .

|

Center’|

Center|

F ′FA

B

A ′

B ′

O

1 \lensSPH

Divergent Lens

The syntax is

\lensSPH [lensType=DVG ,...]

It draws a spherical divergent lens:


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8.2 Options 26

|

Center’|

Center|

F ′FA

B

A ′

B ′ O

1 \lensSPH[lensType=DVG,lensWidth=0.5]

It changes some default values for the options in the same way as for the convergentlens.

8.2 Options

The macro uses the law of Snell

n 1n 2

= sin β sin α

(6)

where the n 1 and n 2 are the refraction numbers with the predened values

n 1 = 1 (7)

n 2 = 1 .41 (8)

and α the incoming abd β the outgoing angle of the ray.The refractionnumbers have the internal names refractA and refractB .


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9 \mirrorCVG 27

9 \mirrorCVG

The syntax is

\mirrorCVG [mirrorType=SPH ]

F A

B

A’

B’

1 \mirrorCVG[mirrorType=SPH]

Without the option mirrorType=SPH you’ll get a parabolic mirror, which is the default.

10 \mirrorDVG

The syntax is

\mirrorDVG [mirrorType=SPH ]

C F A

BPR

PR’

MR MR’

FR FR’

1 \mirrorDVG[mirrorType=SPH]

Without the option mirrorType=SPH you’ll get a parabolic mirror (option PARA).


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11 \ABinterSPHLens 28

11 \ABinterSPHLens

The syntax is

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-3

-2

-1

0

1

2

3

Center Center’

A

B

CD

n1

n2

n1

E

F

1 \ begin {pspicture}[showgrid=true](-6,-3)(6,3)2 \ rput (0,0){\lensSPH[lensType=CVG,lensHeight=8,lensWidth=3,drawing=false]}3 \ qdisk (Center){2pt}\ uput [-90](Center){Center}4 \ qdisk (Center’){2pt}\ uput [-90](Center’){Center’}5 \ pnode (-5,1){A}\ qdisk (A){2pt}\ uput [90](A){A}6 \ pnode (-3,0){B}\ qdisk (B){2pt}\ uput [90](B){B}7 \ psline [linewidth=1.5pt,linecolor=red]{->}(A)(B)8 \ pnode (5,-2.5){C}\ qdisk (C){2pt}\ uput [90](C){C}9 \ pnode (3,-2){D}\ qdisk (D){2pt}\ uput [90](D){D}

10 \ psline [linewidth=1.5pt,linecolor=red]{->}(C)(D)11 \ rput (-4.5,2){\Large $n _1$}\ rput (0,2){\Large $n _2$}\ rput (4.5,2){\Large $n _1$}12 \ABinterSPHLens(A)(B)(Center’){E}\ABinterSPHLens(C)(D)(Center){F}13 \ psline [linestyle=dashed,linecolor=red](B)(E)14 \ psline [linestyle=dashed,linecolor=red](D)(F)15 \ qdisk (E){2pt}\ uput [-20](E){E}\ qdisk (F){2pt}\ uput [-90](F){F}16 \ end {pspicture}

The macro needs two nodes for the rays, the coordinates/nodes of the center/middle of the sperical lens and a name of the intermediate node.In the gure the macro was calledas

\ABinterSPHLens(A)(B)(Center’){E}\ABinterSPHLens(C)(D)(Center){F}

12 \lensSPHRay

The syntax is


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12 \lensSPHRay 30

Center Center’

A B

n 1 n 2 = 3 n 1 = 1

EE’

E”

1 \ begin {pspicture *}[showgrid=true](-5,-3)(7,3)2 \ rput (0,0){\lensSPH[lensType=CVG,lensHeight=8,lensWidth=3,drawing=false]}3 \ qdisk (Center){2pt}\ uput [-90](Center){Center}4 \ qdisk (Center’){2pt}\ uput [-90](Center’){Center’}

5 \ pnode (-4,1){A}\ qdisk (A){2pt}\ uput [90](A){A}6 \ pnode (-2,0.5){B}\ qdisk (B){2pt}\ uput [90](B){B}7 \ rput (-4.5,2.5){\Large $n _1$}\ rput (0,2.5){\Large $n _2=3$}\ rput (4,2.5){\Large $n _1=1$}8 \ multido {\rA=3+-0.5,\rB=2.5+-0.5}{11}{ %9 \lensSPHRay[rightRay=false](-4,\rA)(-2,\rB){1}{3}{F}

10 \ psline [linewidth=1.5pt,linecolor=red]{->}(-4,\rA)(F)11 \ psline [linestyle=dashed,linecolor=red](-4,\rA)(F)(F’)(F’’)12 \psOutLine[linestyle=dashed,linecolor=red](F’)(F’’){FEnd}}13 \ psline [linewidth=1.5pt,linecolor=blue]{->}(A)(B)14 \lensSPHRay[lensType=CVG](A)(B){1}{3}{E}15 \ psline [linestyle=dashed,linecolor=blue](B)(E)(E’)(E’’)16 \ qdisk (E){2pt}\ uput [-20](E){E}\ qdisk (E’){2pt}\ uput [-20](E’){E’}17 \ qdisk (E’’){2pt}\ uput [-20](E’’){E’’}



31/45

13 \reflectionRay 31

13 \reflectionRay

The syntax is

\reflectionRay [Options] ( A )( B ){ NodeName }

This macro calculates the coordinates of the given ray AB on its way out of the mirror.The only senseful option is mirrorType=CVG or mirrorType=DVG . The most importantfact is that the point B must be the one on the mirror. If you do not know it’s coordinates you can use the macro ABinterSPHLens[lensType=CVG](A1)(A2)(Center){NodeName) ,which calculates the coordinates of the intermediate point.

CenterF

A BC

D

1 \ begin {pspicture *}[showgrid=true](-1,-3)(6,3)2 \ rput (0,0){ %3 \mirrorCVG[mirrorType=SPH,mirrorHeight=5,mirrorWidth=0.2,yBottom=-3,yTop=3,drawing=

false,mirrorDepth=3]4 \ qdisk (Center){2pt}\ qdisk (Focus){2pt}\ uput [-90](Center){Center}\ uput [-90](Focus){F}5 \ psline (O)(xRight)}6 \ABinterSPHLens(5,1)(3,1)(Center){C}7 \reflectionRay[mirrorType=CVG-SPH](5,1)(C){D}8 \ qdisk (5,1){2pt}\ uput [-90](5,1){A}\ qdisk (3,1){2pt}\ uput [-90](3,1){B}9 \ qdisk (C){2pt}\ uput [180](C){C}\ qdisk (D){2pt}\ uput [45](D){D}

10 \ psset {linewidth=1.5pt,linecolor=red, arrows =->}11 \ psline (5,1)(3,1)\ psline (3,1)(C)\ psline (C)(D)12 \ end {pspicture *}


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14 Utility Macros 33

Construction for determining the height of an image formed by refraction at a spericalsurface.

|P

|Q

P’

Q’

|C

1 \ begin {pspicture *}[showgrid=true](-13,-3)(3,5)2 \ rput (0,0){ %3 \lensSPH[lensType=CVG,lensHeight=12,lensWidth=10,yBottom=-4,yTop=4,xLeft=-5,xRight=5,

drawing=false]}4 \ psset {linecolor=red,linewidth=1.5pt,dotstyle=|}5 \ pnode (-12,0){P}\ psdots (P)\ uput [-90](P){P}\ pnode (-12,4){Q}\ psdots (Q)\ uput [90](Q){Q}6 \ psline [linecolor=blue,linewidth=3pt, arrows =->](P)(Q)\ psline (P)(xRight)7 \lensSPHRay(Q)(Center’){1}{9}{S1}\lensSPHRay(Q)(-5,0){1}{9}{S2} %8 \ psline (Q)(S1’)\ psline (Q)(S2)(S2’)\ABinterCD(Q)(S1’)(S2)(S2’){Q’}\ pnode (Q’|0,0){P’}9 \ psline [linecolor=blue,linewidth=3pt, arrows =->](P’)(Q’)

10 \ uput [90](P’){P’}\ uput [-90](Q’){Q’}\ psdots (Center’)\ uput [90](Center’){C}11 \ end {pspicture *}

14 Utility Macros

14.1 \eye

Syntax:

\eye

There are no Options for this symbol of an human eye (Figure ?? ). Use the \rput -macroto put the eye elsewhere.

1 \ begin {pspicture}(-1,-0.75)(1,0.75)2 \ rput (1,0){\eye}3 \ end {pspicture}


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21 \rotateFrame 37

\rotateNode{ NodeNameA }{ NodeNameB }{ NodeNameC }{ Degrees }

The coordinates of the nodes A,B,C are changed to the new ones. Negative values arepossible for rotating clockwise.

-1 0 1 2 3 4

0

1

2

3

4

A B

C

A

B

C

1 \ begin {pspicture}[showgrid=true](-1,0)(4,4)

2 \ pnode (1,1){A}\ pnode (3,1){B}\ pnode (2,3){C}3 \ qdisk (A){2pt}\ uput [180](A){A}\ qdisk (B){2pt}\ uput [0](B){

B}4 \ qdisk (C){2pt}\ uput [90](C){C}5 \ psline (A)(B)(C)(A) \rotateTriangle(A)(B)(C){45}6 \ qdisk (A){2pt}\ uput [180](A){A}\ qdisk (B){2pt}\ uput [0](B){

B}7 \ qdisk (C){2pt}\ uput [90](C){C}\ psline [linecolor=red](A)(B

)(C)(A)8 \ psarc [linecolor=red,linewidth=0.5pt]{->}(0,0)

{3.16}{19.47}{64.47}9 \ psarc [linecolor=red,linewidth=0.5pt]{->}(0,0)

{1.41}{45}{90}

10 \ psarc [linecolor=red,linewidth=0.5pt]{->}(0,0){3.61}{56.31}{101.31}


21 \rotateFrame

The syntax is

\rotateFrame{ NodeNameA }{ NodeNameB }{ NodeNameC }{ NodeNameD }{ Degrees }

The coordinates of the nodes A,B,C,D are changed to the new ones. Negative valuesare possible for rotating clockwise.


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22 \arrowLine 38

-2 -1 0 1 2 3 4

0

1

2

3

4

5

A B

CD

A

B

C

D

1 \ begin {pspicture}[showgrid=true](-2,0)(4,5)2 \ pnode (1,1){A}\ pnode (3,1){B}\ pnode (3,3){C}\ pnode

(1,3){D}3 \ qdisk (A){2pt}\ uput [180](A){A}\ qdisk (B){2pt}\ uput

[0](B){B}4 \ qdisk (C){2pt}\ uput [90](C){C} \ qdisk (D){2pt}\ uput

[180](D){D}

5 \ psline (A)(B)(C)(D)(A)6 \rotateFrame(A)(B)(C)(D){45}7 \ qdisk (A){2pt}\ uput [180](A){A}\ qdisk (B){2pt}\ uput

[0](B){B}8 \ qdisk (C){2pt}\ uput [90](C){C} \ qdisk (D){2pt}\ uput

[180](D){D}9 \ psline [linecolor=red](A)(B)(C)(D)(A)


11 \ psarc [linecolor=red,linewidth=0.5pt]{->}(0,0){1.41}{45}{90}

12 \ psarc [linecolor=red,linewidth=0.5pt]{->}(0,0){4.24}{45}{90}



22 \arrowLine

The syntax is

\arrowLine [Options] ( Start )( End ){ ArrowNumber }

Draws a line from Start to End with ArrowNumber arrows inside.

0 1 2 3 4

0

1

2

3

4

1 \ begin {pspicture}[showgrid=true](4,4)2 \arrowLine[linecolor=red](0,0)(4,3){3}3 \arrowLine[linecolor=green,arrowsize=6pt, arrows =-|](0,0)(3,1)

{2}4 \arrowLine[linecolor=blue,arrowOffset=0.75,arrowsize=6pt](4,0)

(0,3){3}5 \ end {pspicture}

22.1 Options

A special option is arrowOffset , which makes it possible to draw lines with different ar-rows. By default the arrows are placed symetrically. This can be moved by arrowOffset . Additionally all other valid options for pslines are possible her, too.


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22.1 Options 39

0 1 2 3 4

0

1

21 \ begin {pspicture}[showgrid=true](4,2)2 \arrowLine[arrowsize=6pt,linecolor=red](0,0.5)(4,0.5){3}3 \arrowLine[arrowsize=6pt,linecolor=red,4 arrows =


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23 List of all optional arguments for pst-optic 40

23 List of all optional arguments for pst-optic

Key Type DefaultlensTwo boolean falselensGlass boolean truedrawing boolean truerightRay boolean falsexLeft ordinary -7.5xRight ordinary 7.5yBottom ordinary -3.0yTop ordinary 3.0lensType ordinary CVGlensColor ordinary lightgraylensWidth ordinary 0.5lensDepth ordinary 1

lensHeight ordinary 5lensScale ordinary 1lensArrowSize ordinary 0.2lensArrowInset ordinary 0.5mirrorType ordinary CVGmirrorDepth ordinary 1mirrorHeight ordinary 5mirrorWidth ordinary 0.25mirrorColor ordinary lightgraymirrorFocus ordinary 8posMirrorTwo ordinary 6mirrorTwoAngle ordinary 45refractA ordinary 1refractB ordinary 1.41XO ordinary 0YO ordinary 0posStart ordinary 0length ordinary 2focus ordinary 2AB ordinary 1OA ordinary -3

arrowOffset ordinary 0nameA ordinary AspotA ordinary 270nameB ordinary BspotB ordinary 90nameF ordinary FspotF ordinary 270nameO ordinary O

Continued on next page


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References 41

Continued from previous page Key Type DefaultspotO ordinary 225nameAi ordinary A’spotAi ordinary 90

nameBi ordinary B’spotBi ordinary 270nameFi ordinary F’spotFi ordinary 270rayColor ordinary redrayWidth ordinary 1.5\pslinewidthAnglePrism ordinary [none]AnglePlan1 ordinary [none]AnglePlan2 ordinary [none]lambda ordinary [none]k ordinary [none]notations boolean true

References

[1] Denis Girou and Manuel Luque. PST-lens - PostScript macros for Generic TeX .ftp://ftp.dante.de/tex-archive/graphics/pstricks/contrib/pst-lens/ ,2001.

[2] Michel Goosens, Frank Mittelbach, Serbastian Rahtz, Denis Roegel, and Herbert Voß. The L A T E X Graphics Companion . Addison-Wesley Publishing Company,

Reading, Mass., 2nd edition, 2007.[3] Laura E. Jackson and Herbert Voß. Die Plot-Funktionen von pst-plot . Die

T E Xnische Komödie , 2/02:27–34, June 2002.

[4] Nikolai G. Kollock. PostScript richtig eingesetzt: vom Konzept zum praktischenEinsatz . IWT, Vaterstetten, 1989.

[5] Manuel Luque. Vue en 3D . http://members.aol.com/Mluque5130/vue3d16112002.zip , 2002.

[6] Herbert Voß. Die mathematischen Funktionen von Postscript. Die T E Xnische

Komödie , 1/02:40–47, March 2002.[7] Herbert Voss. PSTricks Support for pdf . http://PSTricks.de/pdf/pdfoutput.

phtml , 2002.

[8] Herbert Voß. L A T E X in Mathematik und Naturwissenschaften . Franzis-Verlag,Poing, 2006.

[9] Herbert Voß. PSTricks – Grak für T E X und L A T E X . DANTE – Lehmanns,Heidelberg/Hamburg, 5. edition, 2008.

ftp://ftp.dante.de/tex-archive/graphics/pstricks/contrib/pst-lens/http://members.aol.com/Mluque5130/vue3d16112002.ziphttp://members.aol.com/Mluque5130/vue3d16112002.ziphttp://members.aol.com/Mluque5130/vue3d16112002.ziphttp://pstricks.de/pdf/pdfoutput.phtmlhttp://pstricks.de/pdf/pdfoutput.phtmlhttp://pstricks.de/pdf/pdfoutput.phtmlhttp://pstricks.de/pdf/pdfoutput.phtmlhttp://members.aol.com/Mluque5130/vue3d16112002.ziphttp://members.aol.com/Mluque5130/vue3d16112002.zipftp://ftp.dante.de/tex-archive/graphics/pstricks/contrib/pst-lens/


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References 42

[10] Michael Wiedmann and Peter Karp. References for T E X and Friends . http://www.miwie.org/tex-refs/ , 2003.

[11] Timothy Van Zandt. PSTricks - PostScript macros for Generic TeX . http://www.tug.org/application/PSTricks , 1993.

http://www.miwie.org/tex-refs/http://www.miwie.org/tex-refs/http://www.tug.org/application/PSTrickshttp://www.tug.org/application/PSTrickshttp://www.tug.org/application/PSTrickshttp://www.tug.org/application/PSTrickshttp://www.miwie.org/tex-refs/http://www.miwie.org/tex-refs/


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Index

AB, 9\ABinterCD , 35alpha2 , 23AnglePlan1 , 21 , 22AnglePlan2 , 21AnglePrism , 21 , 23\arrowLine , 38arrowOffset , 38\Arrows , 34

B’1 , 12B1, 12\beamLight , 19

CVG, 9 , 25 , 31

drawing , 14DVG, 9 , 25 , 31

Environmentpspicture , 5 , 9 , 19

\eye , 33

F’1 , 12factice , 9

focus , 9

I11 , 12

k , 21 , 22 , 24Keyvalue

CVG, 9DVG, 9PCVG, 9PDVG, 9

Keyword

AB, 9alpha2 , 23AnglePlan1 , 21 , 22AnglePlan2 , 21AnglePrism , 21 , 23arrowOffset , 38drawing , 14focus , 9k , 21 , 22 , 24

lambda , 21length , 34 , 35lensarrowinset , 9lensarrowsize , 9lenscolor , 9lensGlass , 9lensHeight , 9 , 25lensScale , 9lensTwo , 9lensType , 9 , 25lensWidth , 9 , 25mirrorColor , 14mirrorDepth , 14

mirrorFocus , 14mirrorHeight , 14mirrorTwoAngle , 14mirrorType , 27 , 31mirrorWidth , 14nameA , 5nameAi , 5nameB , 5nameBi , 5nameF , 5nameFi , 5nameO , 5notations , 21OA, 9 , 25posMirrorTwo , 14posStart , 34rayColor , 5 , 14refractB , 25rightRay , 29spotA , 5spotAi , 5

spotB , 5spotBi , 5spotF , 5spotFi , 5spotO , 5xBottom , 5 , 14xLeft , 5 , 14XO, 5

43


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Index 44

xRight , 5 , 14xTop , 5 , 14YO, 5

lambda , 21length , 34 , 35\lens , 7 , 9 , 12lensarrowinset , 9lensarrowsize , 9lenscolor , 9\lensCVG , 7\lensDVG , 7lensGlass , 9lensHeight , 9 , 25lensScale , 9\lensSPH , 25

\lensSPHRay , 29lensTwo , 9lensType , 9 , 25lensWidth , 9 , 25

Macro\ABinterCD , 35\arrowLine , 38\Arrows , 34\beamLight , 19\eye , 33\lens , 7 , 9 , 12\lensCVG , 7\lensDVG , 7\lensSPH , 25\lensSPHRay , 29\mirrorCVG , 15 , 27\mirrorCVGRay , 17\mirrorDVG , 27\mirrorDVGRay , 17\newpsstyle , 6

\nodeBetween , 35\Parallel , 12 , 35\planMirrorRay , 17\psBeforeLine , 34\psline , 34\psOutLine , 34\pst-optic , 5\pstextpath , 17\rayInterLense , 12

\reflectionRay , 31\refractionRay , 20\resetOpticOptions , 6\rotateFrame , 37\rotateNode , 36 , 37

\rput , 5 , 9 , 19 , 33\symPlan , 17\telescop , 13 , 35\Transform , 9

mirrorColor , 14\mirrorCVG , 15 , 27\mirrorCVGRay , 17mirrorDepth , 14\mirrorDVG , 27\mirrorDVGRay , 17mirrorFocus , 14mirrorHeight , 14MirrorNode , 17MirrorNode’ , 17MirrorNode” , 17mirrorTwoAngle , 14mirrorType , 27 , 31mirrorWidth , 14multido , 4

nameA , 5nameAi , 5nameB , 5nameBi , 5nameF , 5nameFi , 5nameO , 5\newpsstyle , 6\nodeBetween , 35notations , 21

OA, 9 , 25

opticalAxis , 6Package

multido , 4pst-3d , 4pst-grad , 4pst-math , 4pst-node , 4pst-optic , 4 , 6


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Index 45

pst-plot , 4pst-text , 17pst-xke , 4pstricks , 4 , 5

\Parallel , 12 , 35

PCVG, 9PDVG, 9\planMirrorRay , 17posMirrorTwo , 14posStart , 34\psBeforeLine , 34\psline , 34\psOutLine , 34pspicture , 5 , 9 , 19pst-3d , 4pst-grad , 4pst-math , 4pst-node , 4\pst-optic , 5pst-optic , 4 , 6pst-plot , 4pst-text , 17pst-xke , 4\pstextpath , 17pstricks , 4 , 5

rayColor , 5 , 14\rayInterLense , 12\reflectionRay , 31refractA , 20 , 26refractB , 20 , 25 , 26\refractionRay , 20\resetOpticOptions , 6rightRay , 29\rotateFrame , 37\rotateNode , 36 , 37\rput , 5 , 9 , 19 , 33

SPH, 27spotA , 5spotAi , 5spotB , 5spotBi , 5spotF , 5spotFi , 5spotO , 5

\symPlan , 17Syntax

B’1 , 12B1, 12F’1 , 12

I11 , 12MirrorNode , 17MirrorNode’ , 17MirrorNode” , 17opticalAxis , 6refractA , 20 , 26refractB , 20 , 26

\telescop , 13 , 35\Transform , 9true , 9

ValueCVG, 25 , 31DVG, 25 , 31SPH, 27true , 9

xBottom , 5 , 14xLeft , 5 , 14XO, 5xRight , 5 , 14

xTop , 5 , 14

YO, 5

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