General Physics 102 lab

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lens.zip
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Lens/back.gif

Lens/lens.gif

Lens/Lens.html

Thin Lens (converging/diverging lens/mirrors)

[url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=704.0]Equation for thin lens[/url]: $\\\\frac{1}{p}+\\\\frac{1}{q}=\\\\frac{1}{f}$ where [b]p[/b] is the distance between object and lens, [b]q[/b] is the distance between image and lens, and [b]f[/b] is the focus length of lens.
blue lines trace of light path
green lines backward tracing for virtual image
small red lines distances f and 2*f away from the center of lens.
1st textfield current mouse position (x , y) relative to lens
white vertical line reference line (you can click and drag it left/right)
yellow line light path for paraxial ray assumption(mirror only)
Parameters can be changed :
  1. Select Lens for thin lens effect(default)
  • select mirror for concave/convex mirror effect
default: assume paraxial ray (you can turn it off)
  • press toggle button +/- to change between converging/diverginglens
  • Move the object
click near tip of the object, and drag it to where you like it and release the mouse button.
  • Move the lens/mirror:
click near center of the lens, and drag it to left or right.
if click with left mouse button, only lens will move.
if click with right mouse button, object will move with lens.
  • Change the focus length of the lens/mirror
click near the top/bottom of the lens/mirrir, then drag the mouse . Try it!
  • if you adjust the size of window, parameters reset to default values.
  • you can open more then one window to compare different cases, close the created window to Quit. Press
[b]You are welcomed to check out a wonderful [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1395.0]thin Len flash animation[/url] created by a teacher in Taiwan [/b]
[youtube=E2EmowDS0U4] [youtube=HIZiiqGcwCc]
More advanced topic
[youtube=brTzn9VoGks] [youtube=PlG6ps3i9bo]

This page is translated from Thin Lens (converging/diverging lens/mirrors) by JoeBova ()

Lens/lens2.gif

Lens/LensWindow.class

                synchronized 
                class LensWindow 
                extends java.awt.Frame {
    
                private 
                static boolean 
                working;
    boolean 
                is_applet;
    boolean 
                is_lens;
    int 
                yOffset;
    String[] 
                STR;
    java.awt.TextField 
                textP;
    java.awt.TextField 
                textQ;
    java.awt.TextField 
                textF;
    java.awt.TextField 
                textM;
    java.awt.Checkbox 
                cThin;
    java.awt.Button 
                type;
    java.awt.Dimension 
                area;
    int 
                xc;
    int 
                yc;
    double 
                scale;
    boolean 
                thinMirror;
    boolean 
                objectmove;
    boolean 
                rightClick;
    boolean 
                moveLine;
    int 
                xp;
    int 
                yp;
    String 
                msg;
    java.awt.Dimension 
                offDimension;
    java.awt.Image 
                offImage;
    java.awt.Graphics 
                g;
    int 
                ox;
    int 
                oy;
    int 
                side;
    double 
                ix;
    double 
                iy;
    double 
                magnify;
    boolean 
                inrange;
    boolean 
                normal;
    int 
                lxc;
    int 
                lyc;
    int 
                lh;
    double 
                lr;
    double 
                lf;
    int 
                lwidth;
    boolean 
                moving;
    boolean 
                sizing;
    int[] 
                X;
    int[] 
                Y;
    int 
                cnt;
    int 
                x0;
    int 
                y0;
    int 
                ww;
    int 
                hh;
    
                public void 
                start();
    
                public boolean 
                handleEvent(java.awt.Event);
    void 
                init();
    
                public boolean 
                action(java.awt.Event, Object);
    
                public void 
                reset();
    
                public boolean 
                mouseDown(java.awt.Event, int, int);
    
                public boolean 
                mouseDrag(java.awt.Event, int, int);
    
                public boolean 
                mouseUp(java.awt.Event, int, int);
    
                public boolean 
                mouseMove(java.awt.Event, int, int);
    
                private void 
                writeXY(int, int);
    
                public boolean 
                mouseExit(java.awt.Event, int, int);
    
                public void 
                textInput(int, double);
    
                public void 
                paint(java.awt.Graphics);
    
                public void 
                update(java.awt.Graphics);
    
                private void 
                drawGrid(java.awt.Graphics);
    
                private void 
                writeText(java.awt.TextField, double);
    
                public void 
                drawRay(java.awt.Graphics);
    String 
                d2String(double);
    
                private void 
                drawit(java.awt.Graphics, int, int, int);
    
                public void 
                linit(int, int, int, double);
    boolean 
                lmouseDown(int, int);
    boolean 
                lmouseUp(int, int);
    boolean 
                lmouseDrag(int, int);
    void 
                lmove(int, int);
    void 
                lshow();
    void LensWindow(String, boolean, String[]);
    
                static void 
                <clinit>();
}

Lens/thinLens.class

                public 
                synchronized 
                class thinLens 
                extends java.applet.Applet {
    String 
                buttonText;
    String 
                windowTitle;
    int 
                windowWidth;
    int 
                windowHeight;
    LensWindow 
                m;
    int 
                windowCount;
    java.awt.Color 
                bgColor;
    String 
                rts;
    String[] 
                STR;
    
                public void 
                init();
    
                private void 
                go();
    
                public boolean 
                action(java.awt.Event, Object);
    
                public 
                static void 
                main(String[]);
    
                private void 
                begin();
    
                public void thinLens();
}

Lens/thinLens.java

Lens/thinLens.java

// Modification history
// May 31,1997 fixed bug when object located at focus point 
// May  22,1997 add  paraxial ray option for mirror
// Feb 21,1997 major modification, almost rewritten the whole code
// try without frame => very slow for netscape
// Nov. 3, 1996 impletemt double buffering
//-----------------------------------------------------
// written by Fu-Kwun Hwang
// I hope that you enjoy this applet
// Suggestions? E-mail to  [email protected]
//-----------------------------------------------------
import  java . awt . * ;

public   class  thinLens  extends  java . applet . Applet {
     String  buttonText = "start" ;
     String  windowTitle = "Thin Lens demonstration by Fu-Kwun Hwang(1996)" ;
     int  windowWidth  =   600 ;
     int  windowHeight  =   350 ;
     LensWindow  m ;
     int  windowCount = 0 ;
     Color  bgColor = new   Color ( 0xC8 , 0xDF , 0xD0 );
    
     String  rts , STR [] = { "Reset" , "p" , "q" , "f" , "m" , "lens" , "mirror" , "Paraxial" };
     public   void  init ()   {
        setBackground ( bgColor );
         for ( int  i = 0 ; i < STR . length ; i ++ ){
             if (( rts = getParameter ( STR [ i ])) != null )
                STR [ i ] = new   String ( rts );
         }
         String  str ;
         // get parameters
         if (( str = getParameter ( "buttonText" )) != null )
                buttonText = str ;
         if (( str = getParameter ( "windowTitle" )) != null )
                windowTitle = str ;
         if (( str = getParameter ( "windowWidth" )) != null )
            windowWidth = Integer . parseInt ( str );
         if (( str = getParameter ( "windowHeight" )) != null )
            windowHeight = Integer . parseInt ( str );
         if (( str = getParameter ( "autoStart" )) != null ){
            m  =   new   LensWindow ( windowTitle ,   true , STR );
            go ();
         }
        add ( new   Button ( buttonText ));
     }

     private   void  go (){
        m . resize ( windowWidth , windowHeight );
        m . show ();
        m . start ();
     }

     public   boolean  action ( Event  e , Object  arg )   {
         if   ( e . target  instanceof   Button   &&
                     (( String ) arg ). equals ( buttonText ))   {
            m  =   new   LensWindow ( String . valueOf ( ++ windowCount ) + ":" +
                windowTitle ,   true , STR );
         }
        go ();
         return   true ;
     }
    
     //allow the applet to also run as an application.
     public   static   void  main ( String  args [])   {
         new  thinLens (). begin ();
     }

     private   void  begin ()   {
        m  =   new   LensWindow ( windowTitle ,   false , STR );
        go ();
     }
}
 
class   LensWindow   extends   Frame   {
     boolean  is_applet ;
     boolean  is_lens = true ;
     int  yOffset = 30 ;
     String  STR [];
     LensWindow ( String  title ,   boolean  isapp , String []  s ){
         super ( title );
        is_applet = isapp ;
        setBackground ( Color . lightGray );
        STR = s ;
        init ();
     }
     public   void  start (){
        reset ();
        repaint ();
//      lMirror.hide();
//      cThin.hide();
     }

     public   boolean  handleEvent ( Event  e )   {
         if   ( e . id  ==   Event . WINDOW_DESTROY )   {
            hide ();
            removeAll ();
            dispose ();
             if ( ! is_applet )   System . exit ( 0 );
         }    
         return   super . handleEvent ( e );
     }

     TextField  textP , textQ , textF , textM ; //,textR;
//  Label lMirror;
     Checkbox  cThin ;
     Button  type ;
     Dimension  area ;
     int  xc , yc ;
     double  scale = 10. ;
     void  init (){
         Panel  p = new   Panel ();
//      p.add(textR=new TextField(" X , Y",6));
        p . add ( new   Label ( STR [ 1 ]));
        p . add ( textP = new   TextField ( "10." , 2 ));
        p . add ( new   Label ( STR [ 2 ]));
        p . add ( textQ = new   TextField ( "10." , 2 ));
        p . add ( new   Label ( STR [ 3 ]));
        p . add ( type = new   Button ( "+" ));
        p . add ( textF = new   TextField ( "5." , 2 ));
        p . add ( new   Label ( STR [ 4 ]));
        p . add ( textM = new   TextField ( "1." , 2 ));
         Choice  c ;
        p . add ( c = new   Choice ());
        c . addItem ( STR [ 5 ]);
        c . addItem ( STR [ 6 ]);
        p . add ( new   Button ( STR [ 0 ]));
//      p.add(lMirror=new Label());
        p . add ( cThin = new   Checkbox ( STR [ 7 ]));
        cThin . setState ( true );
        cThin . show ();
        thinMirror = cThin . getState ();
        add ( "North" , p );
        show ();
     }
     boolean  thinMirror = true ;
     public   boolean  action ( Event  ev ,   Object  arg )   {
         if   ( ev . target  instanceof   Button )   {
             String  label  =   ( String ) arg ;
             if ( label . equals ( STR [ 0 ])) reset ();
             else {
                 if ( label . equals ( "+" ))    type . setLabel ( "-" );
                 else   if ( label . equals ( "-" ))   type . setLabel ( "+" );
                lf *=- 1. ;
                repaint ();
             }
         } else   if (  ev . target  instanceof   TextField ){
             String  label  =   ( String ) arg ;
             double  value ;
            value = Double . valueOf ( label ). doubleValue ();
             if ( ev . target == textP )
                textInput ( 1 , value );
             else   if ( ev . target == textQ )
                textInput ( 2 , value );
             else   if ( ev . target == textF )
                textInput ( 3 , value );
             else   if ( ev . target == textM )
                textInput ( 4 , value );
                repaint ();
         } else   if ( ev . target  instanceof   Choice ){
             String  label  =   ( String ) arg ;
             if ( label . equals ( STR [ 5 ])){
                is_lens = true ;
//              lMirror.hide();
//              cThin.hide();
             } else {
                is_lens = false ;
//              lMirror.show();
                cThin . show ();
                show ();
             }
            lshow ();
            repaint ();
         } else   if ( ev . target  instanceof   Checkbox ){
            thinMirror = cThin . getState ();
            lshow ();
            repaint ();
         }
         return   true ;
     }

     public   void  reset ()   {
        area = size ();
        area . height -= yOffset ;
        xc = area . width / 2 ;
        yc = area . height / 2 ;
         double  ff = 10. * scale ;
        type . setLabel ( "+" );
        textF . setText ( Double . toString ( ff ));
        linit ( xc , yc ,( int )( 0.7 * yc ), ff );
        xc -= ( int )( 2. * lf );   // initial object position
        yc = yc * 3 / 4 ;
        repaint ();
     }

     boolean  objectmove = false , rightClick = false , moveLine = false ;
     int  xp , yp ; // vertical reference line
     public   boolean  mouseDown ( Event  e ,   int  x ,   int  y ){
        y -= yOffset ;
         if ( Math . abs ( x - xp ) < 5 ) moveLine = true ;
         else   if ( ! lmouseDown ( x , y )){
             if ( Math . abs ( x - xc ) < 5   ){
                xc = x ;
                yc = y ;
                repaint ();
                objectmove = true ;
             }
         }
         if ( e . modifiers == Event . META_MASK ) //"Right Click, ";
                rightClick = true ;
         return   true ;
     }
    
     public   boolean  mouseDrag ( Event  e ,   int  x ,   int  y ){
        y -= yOffset ;
         if ( working ) return   true ;
         if ( lmouseDrag ( x , y )){
             if ( rightClick ) xc = lxc - ox ; // also move objects
            repaint ();   // change lens
         } else   if ( objectmove ){   // move object
             if ( ! is_lens  &&  x > lxc  ||  lh < Math . abs ( y - lyc )   ) return   true ;
            xc = x ;
            yc = y ;
             if ( rightClick ) lxc = xc + side * ox ; // also move lens
            writeXY ( x , y );
            repaint ();
         } else   if   ( moveLine ){
            xp = x ;
            yp = y ;
            writeXY ( x , y );
            repaint ();
         }
         return   true ;
     }    

     public   boolean  mouseUp ( Event  e ,   int  x ,   int  y ){
        y -= yOffset ;
        lmouseUp ( x , y );
        objectmove = false ;
        rightClick = false ;
        moveLine = false ;
        repaint ();
         return   true ;
     }

     public   boolean  mouseMove ( Event   evt ,   int   x ,   int   y ){
        y -= yOffset ;
         if ( working ) return   true ;
         if ( ! objectmove ) writeXY ( x , y );
        repaint ();
         return   true ;
     }
     String  msg = " X , Y" ;
     private   void  writeXY ( int  x ,   int  y ){
         //textR.setText(
            msg =
             Double . toString (( int )( 10. * ( lxc - x ) / scale ) / 10. ) +
             "," +
             Double . toString (( int )( 10. * ( lyc - y ) / scale ) / 10. );
     }

     public   boolean  mouseExit ( Event   evt ,   int   x ,   int   y ){
        y -= yOffset ;
//      textR.setText(" X , Y");
        msg = " X , Y" ;
        repaint ();
         return   true ;
     }

     public   void  textInput ( int  type , double  value ){
         switch   ( type )   {
         case   1 :   // P
            xc = lxc - ( int )( value * scale );
             break ;
         case   2 :   // Q
            xc = lxc - ( int )( 1. / ( 1. / lf - 1. / ( scale * value )));
             break ;
         case   3 :   // F
            lf = value * scale ;
             break ;
         case   4 :   // M
            xc = lxc - ( int )( Math . abs (( 1. - 1. / value ) * lf ));
             break ;
         }
     }

     Dimension  offDimension ;
     Image  offImage ;
     Graphics  g ;

     public   void  paint ( Graphics  gs ){
        update ( gs );
     }
     private   static   boolean  working = false ;
     public   void  update ( Graphics  gs ){
        working = true ;
        area = size ();
        area . height -= yOffset ;
         if   (   ( g  ==   null )   // if resize window
                 ||   ( area . width  !=  offDimension . width )
                 ||   ( area . height  !=  offDimension . height )   )   {
            offDimension  =  area ;
            offImage  =  createImage ( area . width ,  area . height );
            g  =  offImage . getGraphics ();
            xp = area . width - 50 ;
            reset ();
         }
         //Erase the previous image.
        g . setColor ( getBackground ());
        g . fillRect ( 0 ,   0 ,  area . width ,  area . height );
        g . setColor ( Color . black );
        g . drawString ( msg , 5 , 15 + yOffset );
        g . drawLine ( 0 , lyc , area . width , lyc );
        drawGrid ( g );
        drawRay ( g );
        lshow ();
        g . setColor ( Color . white );
        g . drawLine ( xp , 30 , xp , area . height - 30 );
         if ( moveLine ) g . drawLine ( xp - 15 , yp , xp + 15 , yp );
        gs . drawImage ( offImage ,   0 ,  yOffset ,   this );
        working = false ;
     }

     private   void  drawGrid ( Graphics  g ){
        g . setColor ( Color . gray );
         int  i , j ;
         for ( i = lxc , j = 0 ; i > 0 ; j ++ , i = lxc - ( int )( j * scale ))
            g . drawLine ( i , lyc - 2 , i , lyc + 2 );
         for ( i = lxc , j = 0 ; i < area . width ; j ++ , i = lxc + ( int )( j * scale ))
            g . drawLine ( i , lyc - 2 , i , lyc + 2 );
         //g.setColor(Color.black);
     }

     private   void  writeText ( TextField  obj , double  value ){
        value = ( double )(( int )( 10. * value / scale )) / 10. ;
         //formated output, keep same digits outputs after .
        obj . setText ( Double . toString ( value ));
     }

     int  ox , oy , side ;       // object position
     double  ix , iy ;             // image position
     double  magnify ;
     boolean  inrange , normal ;
     public   void  drawRay ( Graphics  g ){
         if ( lxc > xc ){
            ox = lxc - xc ;
            side = 1 ;
         } else {
            ox = xc - lxc ;
            side =- 1 ;
         }
        oy = lyc - yc ;
         if ( ox == lf ){ // located at focus point
            normal = false ;
            textQ . setText ( "Inf" );
         } else   {
            normal = true ;
            ix = 1. / ( 1. / lf - 1. / ox );
            writeText ( textQ , ix );
         }
        magnify =- ix / ox ;
         // write P,Q,F
        writeText ( textP , Math . abs ( lxc - xc ));
        writeText ( textF , Math . abs ( lf ));
        textM . setText ( d2String ( magnify ));
         int  x1 , y1 , x2 , y2 ;   // ray paths
        x1 = lxc - side * ox ;
        y1 = lyc - oy ;
         if ( normal ) iy = magnify * oy ;
         else { // May 31,1997
             double  mag2 =- 100. * magnify / Math . abs ( magnify );
            iy =- mag2 * oy ;
            ix = mag2 * ox ;
         }
        y2 = lyc - ( int ) iy ;
         //draw object
        g . setColor ( Color . blue );
        drawit ( g , x1 , lyc , oy );
         if ( lh > Math . abs ( iy )) inrange = true ;
         else  inrange = false ;
         if ( is_lens ){ // lens
            x2 = lxc + side * ( int ) ix ;
            g . drawLine ( x1 , y1 , lxc , y1 );         //1-1 平行入射光
             if ( magnify < 0 ){
                g . drawLine ( lxc , y1 , x2 , y2 );     //1-2
                g . drawLine ( x1 , y1 , x2 , y2 );          //2     穿過透鏡中心
                 if ( inrange ){
                    g . drawLine ( x1 , y1 , lxc , y2 );     //3-1   穿過焦點入射光
                    g . drawLine ( lxc , y2 , x2 , y2 );     //3-2   平行主軸
                 }
                g . setColor ( Color . blue );
             } else {
                 if ( lf > 0 ){         // converging lens
                    g . drawLine ( lxc , y1 , lxc + 2 * side * ( int ) lf , lyc + oy );     //1-2
                    g . drawLine ( x1 , y1 , lxc - side * ( int ) ix , lyc + ( int ) iy );   //2-1
                     if ( inrange )   {
                        g . drawLine ( x1 , y1 , lxc , lyc - ( int ) iy );                            //3-1
                        g . drawLine ( lxc , y2 , lxc + 2 * side * ( int ) lf , y2 );             //3-2
                     }
                    g . setColor ( Color . green );
                    g . drawLine ( x1 , y1 , x2 , y2 );                                  //2-2
                    g . drawLine ( lxc , y1 , x2 , y2 );                             //1-3
                     if ( inrange )  g . drawLine ( lxc , y2 , x2 , y2 );                             //3-3
                 } else {                // diverging lens
                    g . drawLine ( lxc , y1 , lxc - 2 * side * ( int ) lf , lyc - 3 * oy );   //1-2
                    g . drawLine ( x1 , y1 , lxc + side * ox , lyc + ( int ) oy );    //2
                     if ( inrange ){
                        g . drawLine ( x1 , y1 , lxc , y2 );                                         //3-1
                        g . drawLine ( lxc , y2 , lxc - 2 * side * ( int ) lf , y2 );     //3-2
                     }
                    g . setColor ( Color . green );
                    g . drawLine ( lxc , y1 , lxc + side * ( int ) lf , lyc );      //1-3
                     if ( inrange )  g . drawLine ( lxc , y2 , lxc + side * ( int ) ix , y2 );           //3-3
                 }
             }
         } else { // mirror
             double  angle = Math . asin ( oy / lr );
             double  dw = 0. , dw2 ;
             int  xx , xx2 , yy ;
            x2 = lxc - ( int ) ix ;
             if ( ! thinMirror ) dw = lr * ( 1. - Math . cos ( angle ));
            xx = lxc - ( int ) dw ;
            angle *= 2. ;
             if ( lf > 0 ){ // concave mirror 凹面鏡
                 boolean  within ;
                g . drawLine ( x1 , y1 , lxc , lyc );   //2-1 物 通過 鏡面中心
                yy = lyc - ( int )( lr * oy / ( lr - ox ));
                 double  mm = iy / ( - ix + lr ), xt = 0. ;
                 if ( ! thinMirror )  xt = lr * ( 1. / Math . sqrt ( 1. + mm * mm ) - 1. );
                 if (   ( within = ( Math . abs ( mm * ( xt + lr )) < lh )) &&   ! thinMirror )
                    g . drawLine ( x1 , y1 , lxc + ( int ) xt , yy = lyc - ( int )( mm * ( xt + lr ))); //4-1垂直入射鏡面
                xx2 = lxc + ( int )( iy * ( lf - ox ) / oy - lf );
                 if ( oy > 0 ) side = 1 ; else  side =- 1 ;
                 if ( oy * iy > 0 ){ //虛像
                     if ( ! thinMirror ) g . drawLine ( x1 , y1 , lxc - ( int ) lr , lyc ); //4-2 垂直入射
                     else  g . drawLine ( lxc - ( int )( 2. * lf ), lyc , lxc , yy = lyc - ( int )( iy * 2. * lf / ( 2. * lf - ix )));
                    g . drawLine ( lxc , lyc , lxc - 2 * ox , lyc + 2 * oy ); //2-2 鏡心反射
                    g . setColor ( Color . green );
                    g . drawLine ( lxc , lyc , x2 , y2 ); //2-3 
                    g . drawLine ( lxc + ( int ) xt , yy , x2 , y2 ); //2-1
                    g . setColor ( Color . blue );
                    g . drawLine ( x1 , y1 , xx , y1 ); //1-1 平行入射光
                     if ( ! thinMirror ) g . drawLine ( xx , y1 , lxc - ( int ) lr , lyc - oy + ( int )( Math . tan ( angle ) * ( lr - dw ))); //1-2
                    g . setColor ( Color . green );
                     if ( ! thinMirror ){
                        g . drawLine ( xx , y1 , lxc - ( int ) ix , lyc - oy - ( int )( Math . tan ( angle ) * ( - ix + dw ))); //1-3
                        g . setColor ( Color . yellow );
                        g . drawLine ( lxc - ( int ) lf , lyc , x2 , y2 );
                     } else {
                        g . drawLine ( lxc , y1 , x2 , y2 );
                        g . drawLine ( lxc , yy , x2 , y2 );
                        g . setColor ( Color . blue );
                        g . drawLine ( lxc , y1 , lxc - ( int ) lf , lyc );
                     }
                 } else { //實像
                    g . drawLine ( lxc , lyc , x2 , y2 ); //2-2 鏡面中心--像
                     if ( within &&! thinMirror ) g . drawLine ( x1 , y1 , x2 , y2 ); //4-2
                    g . drawLine ( x1 , y1 , xx , y1 ); //1-1 平行入射光
                     if ( ! thinMirror ){
                        g . drawLine ( xx , y1 , lxc - ( int ) ix , lyc - oy + side * ( int )( Math . abs ( Math . tan ( angle )) * ( ix - dw ))); //1-2
                        g . setColor ( Color . yellow );
                     }
                    g . drawLine ( xx , y1 , lxc , yy = lyc + ( int )( lf * iy / ( ix - lf )));
                    g . drawLine ( x2 , y2 , lxc , yy );
                     if ( inrange ){
                        g . drawLine ( x1 , y1 , lxc , yy = lyc + ( int )( lf * oy / ( ox - lf ))); //3-1
                        g . drawLine ( x2 , y2 , lxc , yy ); //3-2
                     }
                 }
                 if ( ! thinMirror ){
                    g . setColor ( Color . white );
                    g . drawLine ( lxc - ( int ) lr , lyc , xx , y1 );
                 }
             } else { // convex mirror
                dw2 = lr * ( 1. - Math . cos ( Math . asin ( oy / ( lr + ox ))));
                yy = lyc + ( int )(( 2 * lf + dw2 / 2. ) * oy / ( ox - 2. * lf ));
                g . drawLine ( x1 , y1 , xx = lxc + ( int ) dw2 , yy ); //2垂直射向鏡面
                g . drawLine ( x1 , y1 , lxc , lyc ); //3 通過鏡面中心
                g . drawLine ( lxc - 2 * ox , lyc + 2 * oy , lxc , lyc ); //3-1
                g . setColor ( Color . green );
                 if ( ! thinMirror ) g . drawLine ( lxc + ( int ) dw2 , yy , lxc + ( int ) lr , lyc ); //2-1
                 else  g . drawLine ( xx , yy , lxc - ( int )( 2 * lf ), lyc );
                g . drawLine ( lxc , lyc , x2 , y2 ); //3-2
                g . setColor ( Color . blue );
                g . drawLine ( x1 , y1 , xx = lxc + ( int )( dw ), y1 ); //1-1 平行入射光
                 if ( ! thinMirror ) g . drawLine ( lxc + ( int )( dw + lf ), y1 + ( int )( lf * Math . tan ( angle )), xx , y1 );
                 else  g . drawLine ( lxc ,( int ) y1 , lxc + ( int )( 2 * lf ), y1 - 2 * oy );
                 if ( ! thinMirror ){
                    g . setColor ( Color . white );
                    g . drawLine ( lxc + ( int )( 2 * dw - lr ), 2 * y1 - lyc , lxc - ( int )( 2 * lf ), lyc ); //通過焦點
                 }
                g . setColor ( Color . green );
                 if ( ! thinMirror ){
                    g . drawLine ( xx , y1 , lxc + ( int )( dw - lf ), y1 - ( int )( lf * Math . tan ( angle )));
                    g . setColor ( Color . yellow );
                 }
                g . drawLine ( lxc , y1 , lxc - ( int ) lf , lyc );
             }
         }
         if ( oy * iy > 0 ) g . setColor ( Color . green );
         else  g . setColor ( Color . darkGray );
        drawit ( g , x2 , lyc ,( int ) iy );   // draw image
     }
     String  d2String ( double  d ){
         float  d2 = ( float )(( int )( 100. * d ) / 100. );
         String  str = String . valueOf ( d2 );
         if ( str . indexOf ( "." ) ==- 1 ) str += ".0" ;
         return  str ;
     }

     private   void  drawit ( Graphics  g , int  x , int  y , int  height ){
         // for object and image 
         int  x1 , y1 , width = 2 , sign = 1 ;
        x1 = x - width / 2 ;
         if ( height < 0 ){  
            sign =- 1 ;
            y1 = y ;
         } else  y1 = y - height ;
        g . fillRect ( x1 , y1 , width , sign * height );
        y1 = y - height ;
        width = 2 * width ;
        sign *= 2 ;
         // draw hats
        g . drawLine ( x , y1 , x + width , y1 + sign * width );
        g . drawLine ( x , y1 , x - width , y1 + sign * width );
     }
     int  lxc , lyc , lh ;   // (xc,yc):center position, h:height of lens
     double  lr , lf ;         // focusLength*2;
     int  lwidth ;       // half/quater width of lens

     public   void  linit ( int  x ,   int  y , int  hi , double  fi ){
        lxc = x ;  lyc = y ;
        lr = Math . abs ( 2. * fi );
        lf = fi ;
         if ( hi < 10 ) lh = 10 ;   // minimum height of lens
         else   if ( hi > lr )  lh = ( int ) lr - 10 ;
             else  lh = hi ;
//      if(!is_lens && lf<0)type.setLabel("-");
//      else type.setLabel("+");
     }

     boolean  moving = false ;
     boolean  sizing = false ;
     boolean  lmouseDown ( int  x , int  y ){
         if ( Math . abs ( x - lxc + ww ) < lwidth ){
             if ( Math . abs ( y - lyc ) < lh / 2. ) moving = true ;   // move lens
                 if (( Math . abs ( y - lyc - lh ) < lh / 2. )   ||   ( Math . abs ( y - lyc + lh ) < lh / 2. ))
                    sizing = true ;   // change lens size/shape
                 else  sizing = false ;
             return   true ;
         } else   if ( ! is_lens  &&  x > lxc  &&   ( x - lxc ) < lwidth  &&   Math . abs ( y - lyc ) < lwidth ){
             return  moving = true ;
         }
         return   false ;        
     }

     boolean  lmouseUp ( int  x , int  y ){
        sizing = false ; // back to normal
        moving = false ;
         return   true ;
     }

     boolean  lmouseDrag ( int  x , int  y ){
         boolean  done  =   true ;
         if ( sizing ){   // change lens size/shape
             double  dx , dy ;
             double  sign = 1. ;
             if ( is_lens ){
                dx = Math . abs ( x - lxc );
             //  if(lf<0)sign=-1;
             } else  dx = lxc - x ;
             if ( type . getLabel (). compareTo ( "-" ) == 0 ) sign =- 1. ;
            dy = Math . abs ( y - lyc );
            linit ( lxc , lyc ,( int ) dy , sign * Math . abs ( dy * dy / dx + dx ) / 4. );
         } else   if ( moving ) lmove ( x , lyc );   // move lens
         else  done = false ;
         return  done ;
     }

     void  lmove ( int  x ,   int  y ){
         if ( ! is_lens  &&  x < xc ) return ;
        lxc = x ;
        lyc = y ;
        show ();
     }
     int  X [], Y [], cnt = 0 ;
     int  x0 , y0 , ww , hh ;
     void  lshow (){
         if ( ! sizing  && (  is_lens  ||  thinMirror )   )  lr = ( 3. + lh * lh / 3. ) / 4 ;
         //else if (!sizing && thinMirror)lr=(3.+lh*lh/3.)/4;
         else  lr = Math . abs ( 2. * lf );
         // 3. is the half width of lens
         if ( lr < lh ) lh = ( int )( 0.95 * lr );
         double  angle = Math . asin (( double ) lh / lr );
        lwidth = ( int )( lr * ( 1. - Math . cos ( angle )));
        g . setColor ( Color . red );
         if ( is_lens  &&  lf > 0 ) if ( sizing ) g . drawOval ( lxc - lwidth , lyc - lh , 2 * lwidth , 2 * lh );
         else  g . fillOval ( lxc - lwidth , lyc - lh , 2 * lwidth , 2 * lh );
         else {
             double  x0 , y0 ;
             double  c = Math . PI - angle , dc ;
             int  ncnt = 100 ; //(int)(lr*c/15.)+1;
             int  ncnt2 = 2 * ncnt ;
            x0 = lxc + lwidth / 2 + lr ;
            y0 = lyc ;
             if ( ncnt > cnt ){
                X = new   int [ ncnt2 ];
                Y = new   int [ ncnt2 ];
                cnt = ncnt ;
             }
             //g.drawString(String.valueOf(ncnt),100,100);
            ncnt2 -= 1 ;
            dc = 2. * angle / ( ncnt - 1 );
             if ( is_lens ){
                 for ( int  i = 0 ; i < ncnt ; i ++ ){
                    X [ i ] = ( int )( x0 + lr * Math . cos ( c ));
                    Y [ ncnt2 - i ] = Y [ i ] = ( int )( y0 + lr * Math . sin ( c ));
                    X [ ncnt2 - i ] = ( int )( 2 * lxc ) - X [ i ];
                    c += dc ;
                 }
             } else { // mirror
                 if ( lf > 0 ){ // concave mirror
                    ww = lwidth ;
                    x0 = lxc - lr + 1 ;
                     for ( int  i = 0 ; i < ncnt ; i ++ ){
                        X [ i ] = ( int )( x0 - lr * Math . cos ( c ));
                        Y [ ncnt2 - i ] = Y [ i ] = ( int )( y0 + lr * Math . sin ( c ));
                        X [ ncnt2 - i ] = X [ i ] + lwidth ;
                        c += dc ;
                     }
                 } else {   //convex mirror
                    ww =- lwidth ;
                    x0 = lxc + lr ;
                     for ( int  i = 0 ; i < ncnt ; i ++ ){
                        X [ i ] = ( int )( x0 + lr * Math . cos ( c ));
                        Y [ ncnt2 - i ] = Y [ i ] = ( int )( y0 + lr * Math . sin ( c ));
                        X [ ncnt2 - i ] = X [ i ] + lwidth ;
                        c += dc ;
                     }
                 }
             }
            X [ ncnt2 ] = X [ 0 ];
            ncnt2 ++ ;
             if ( ! is_lens ){
                g . setColor ( Color . black );
                 if ( thinMirror ){ if ( sizing ) g . drawPolygon ( X , Y , ncnt2 );
                 else  g . fillPolygon ( X , Y , ncnt2 );
                 } else  g . drawPolygon ( X , Y , ncnt2 );
             } else     if ( sizing ) g . drawPolygon ( X , Y , ncnt2 );
             else  g . fillPolygon ( X , Y , ncnt2 );
         }
        g . setColor ( Color . red );
        g . drawLine ( lxc , lyc - 5 , lxc , lyc + 5 );
         // draw at +/- f, +/- 2f, 
         int  delta = ( int ) lf , xa , ya = lyc - 5 , yb = lyc + 5 ;
        g . drawLine ( xa = lxc - delta , ya , xa , yb );
        delta = ( int )( 2. * lf );
        g . drawLine ( xa = lxc - delta , ya , xa , yb );
         if ( is_lens ){
            g . drawLine ( xa = lxc + delta , ya , xa , yb );
            delta = ( int )( lf );
            g . drawLine ( xa = lxc + delta , ya , xa , yb );
         }        
         if ( is_lens ){
             if ( ! sizing && inrange ){
                g . setColor ( Color . black );
                 //if(side>0.)ww=lwidth;//  draw ray path in lens approximately
                 //else ww=-lwidth;
                ww = lwidth ;
                g . drawLine ( lxc - side * ww * 3 / 4 , lyc - oy , lxc + side * ww , lyc + ( int )( oy * ( ww - lf ) / lf ));
                g . drawLine ( lxc - side * ww , lyc - ( int )( iy * ( - ww + lf ) / lf ), lxc + side * ww * 3 / 4 , lyc - ( int )( iy ));
             }
            ww = 0 ; // for lens
         }
     }
}