/*
  =================================================
  Light propagation in a spherical droplet, forming
  primary and secondary rainbows
  -------------------------------------------------
  Created by Søren Peo Pedersen - see my user page
  at http://da.wikipedia.org/wiki/Bruger:Peo
  =================================================
  */
  
  #declare PrimaryRays=yes;
  // Use "no" for light propagation in secondary rainbow,
  // or "yes" for light propagation in primary rainbow.
  
  #if (PrimaryRays)
    
    // Rendition of light propagation for primary rainbow's light propagation:
    #local pgmSpectrum1=pigment { // Pigment for first spectrum "fan-out"
      radial
      color_map {
        [0.0000 color rgbt <.5,0,1,1>]
        [0.1429 color rgbt <.5,0,1,.5>]
        [0.2857 color rgbt < 0,0,1,.5>]
        [0.4286 color rgbt < 0,1,1,.5>]
        [0.5714 color rgbt < 0,1,0,.5>]
        [0.7143 color rgbt < 1,1,0,.5>]
        [0.8571 color rgbt < 1,0,0,.5>]
        [1.0000 color rgbt < 1,0,0,1>]
        }
      frequency 200
      rotate <90,0,-13.1>
      translate <-3.806586,1.70909106,0>
      scale 1/1.67
      }
    
    #local pgmSpectrum2=pigment { // Pigment for second spectrum "fan-out"
      radial
      color_map {
          [0.0000 color rgbt <1,1,1,1>]
          [0.5000 color rgbt <1,1,1,0>]
          [1.0000 color rgbt <1,1,1,1>]
          }
      frequency 200
      rotate <90,0,-13.1>
      translate <-3.806586,1.70909106,0>
      scale 1/1.67
      }
    
    union {
      difference {  // Incoming white light beam
        box {<-100,.67,-.0001>,<0,.83,.0001>}
        sphere {0,1}
        pigment {
          gradient y
          color_map {
            [0.0 color rgbt<1,1,1,1>]
            [0.2 color rgbt<1,1,1,.9>]
            [0.3 color rgbt<1,1,1,.5>]
            [0.5 color rgbt<1,1,1,0>]
            [0.7 color rgbt<1,1,1,.5>]
            [0.8 color rgbt<1,1,1,1,.9>]
            [1.0 color rgbt<1,1,1,1>]
            }
          scale .16
          translate <0,.67,0>
          }
        finish {
          ambient 1
          diffuse 0
          }
        no_shadow
        no_reflection
        rotate <0,0,-20.825>
        }
        
      difference {  // First "rainbow-colored" beam inside droplet
        cylinder {<0,0,-.0001>,<0,0,.0001>,1} // Disc w. same diameter as droplet
        plane {<0,1,0>,0 rotate <0,0,-14.9> translate <-0.7141428,.7,0>}  // Cut-off
        plane {<0,-1,0>,0 rotate <0,0,-13.1> translate <-0.6,.8,0>}       // boundaries
        pigment {
          gradient x
          pigment_map {
            [0 pgmSpectrum2]
            [1 pgmSpectrum1]
            }
          scale 1.67
          translate <-.7,0,0>
          }
        finish {
          ambient 1
          diffuse 0
          }
        rotate <0,0,-20.825>
        no_shadow
        no_reflection
        }
      
      merge {       // Second "rainbow-colord" beam inside droplet - "crossing over" itself
        difference {  // The portion to the left of the "cross-over" point
          cylinder {<0,0,.0003>,<0,0,.0002>,1}  // Droplet-sized disc
          plane {<0,-1,0>,0 rotate <0,0,45> translate <1,.12,0>}  // Cut-off
          plane {<0,1,0>,0 rotate <0,0,25> translate <1,-.09,0>}  // boundaries                    
          }
        difference {  // The portion to the right of the "cross-over" point
          cylinder {<0,0,.0003>,<0,0,.0002>,1}  // Droplet-sized disc
          plane {<0,1,0>,0 rotate <0,0,45> translate <1,.12,0>}   // Cut-off
          plane {<0,-1,0>,0 rotate <0,0,25> translate <1,-.09,0>} // boundaries                    
          }
        pigment {
          radial
          color_map {
            [0.0000 color rgbt <.5,0,1,1>]
            [0.1429 color rgbt <.5,0,1,.5>]
            [0.2857 color rgbt < 0,0,1,.5>]
            [0.4286 color rgbt < 0,1,1,.5>]
            [0.5714 color rgbt < 0,1,0,.5>]
            [0.7143 color rgbt < 1,1,0,.5>]
            [0.8571 color rgbt < 1,0,0,.5>]
            [1.0000 color rgbt < 1,0,0,1>]
            }
          frequency 18
          rotate <90,0,-35>
          translate <.606514871,-.273485129,0>
          }
        finish {
          ambient 1
          diffuse 0
          }
        no_shadow
        no_reflection
        }
          
      difference {  // The "rainbow-colored light" leaving the droplet at lower left corner:
        box {<-100,0,-.0001>,<0,10,.0001> rotate <0,0,32.825> translate <-.113,-.994,0>}
        plane {<0,-1,0>,0 rotate <0,0,8.825> translate <-.565,-.805,0>}
        cylinder {<0,0,-1>,<0,0,1>,1}   // Cut away part that would fall inside droplet
        pigment {
          radial
          color_map {
            [0.0000 color rgbt < 1,0,0,1>]
            [0.1429 color rgbt < 1,0,0,0>]
            [0.2857 color rgbt < 1,1,0,0>]
            [0.4286 color rgbt < 0,1,0,0>]
            [0.5714 color rgbt < 0,1,1,0>]
            [0.7143 color rgbt < 0,0,1,0>]
            [0.8571 color rgbt <.5,0,1,0>]
            [1.0000 color rgbt <.5,0,1,1>]
            }
          frequency 15
          rotate <-90,0,20.825>
          translate <0.416125,-.65268,0>
          }
        finish {ambient 1 diffuse 0}
        no_shadow
        no_reflection
        }
      }
      
  #else
  
  // Rendition of light propagation for secondary rainbow's light propagation:
  #local pgmSpectrum1=pigment { // Pigment for "rainbow-colored" part of first beam inside droplet
    radial
    color_map {
      [0.0000 color rgbt < 1,0,0,1>]
      [0.1429 color rgbt < 1,0,0,.5>]
      [0.2857 color rgbt < 1,1,0,.5>]
      [0.4286 color rgbt < 0,1,0,.5>]
      [0.5714 color rgbt < 0,1,1,.5>]
      [0.7143 color rgbt < 0,0,1,.5>]
      [0.8571 color rgbt <.5,0,1,.5>]
      [1.0000 color rgbt <.5,0,1,1>]
      }
    frequency 200
    rotate <90,0,-.9>
    translate <-3.7364,-0.69606,0>
    scale 1/1.7
    }
  
  #local pgmSpectrum2=pigment { // Pigment for white part of first "rainbow-colored" beam inside droplet
    radial
    color_map {
      [0.0000 color rgbt <1,1,1,1>]
      [0.5000 color rgbt <1,1,1,0>]
      [1.0000 color rgbt <1,1,1,1>]
      }
    frequency 200
    rotate <90,0,-.9>
    translate <-3.8364,-0.69606,0>
    scale 1/1.7
    }
    
    union {
    difference {    // White-to "rainbow-colored" beam inside droplet
      cylinder {<0,0,-.0001>,<0,0,.0001>,1}
      plane {<0, 1,0>,0 rotate <0,0,-.9> translate <-.657,-.757,0>}
      plane {<0,-1,0>,0 rotate <0,0, .9> translate <-.777,-.637,0>}
      pigment {
        gradient x
        pigment_map {
          [0 pgmSpectrum2]
          [1 pgmSpectrum1]
          }
        scale 1.7
        translate <-.8,0,0>
        }
      finish {ambient 1 diffuse 0}
      no_shadow
      no_reflection
      }
    merge {    
      difference {  // Lower part of self-crossing beam at right-ahdn side inside droplet
        cylinder {<0,0,.0002>,<0,0,.0003>,1}
        plane {< 1,0,0>,0 rotate <0,0,-6 > translate <.622,-.692,0>}
        plane {<-1,0,0>,0 rotate <0,0, 6 > translate <.787,-.727,0>}
        }
      difference {  // Upper part of self-crossing beam at right-ahdn side inside droplet
        cylinder {<0,0,.0002>,<0,0,.0003>,1}
        plane {<-1,0,0>,0 rotate <0,0,-6 > translate <.622,-.692,0>}
        plane {< 1,0,0>,0 rotate <0,0, 6 > translate <.787,-.727,0>}
        }
      pigment {
        radial
        color_map {
          [0.0000 color rgbt < 1,0,0,1>]
          [0.1429 color rgbt < 1,0,0,.5>]
          [0.2857 color rgbt < 1,1,0,.5>]
          [0.4286 color rgbt < 0,1,0,.5>]
          [0.5714 color rgbt < 0,1,1,.5>]
          [0.7143 color rgbt < 0,0,1,.5>]
          [0.8571 color rgbt <.5,0,1,.5>]
          [1.0000 color rgbt <.5,0,1,1>]
          }
        frequency 30
        rotate <90,0,84>
        translate <.702661,0.075435,0>                        
        }
      finish {ambient 1 diffuse 0}
      no_shadow
      no_reflection
      }
  
    merge {   // Right-hand part of self-crossing beam at top of droplet
      difference {
        cylinder {<0,0,.0004>,<0,0,.0005>,1}
        plane {<0,-1,0>,0 rotate <0,0, 6 > translate <.637,.777,0>}
        plane {<0, 1,0>,0 rotate <0,0,-6 > translate <.772,.642,0>}
        }
      difference {  // Left-hand part of self-crossing beam at top of droplet
        cylinder {<0,0,.0004>,<0,0,.0005>,1}
        plane {<0, 1,0>,0 rotate <0,0, 6 > translate <.637,.777,0>}
        plane {<0,-1,0>,0 rotate <0,0,-6 > translate <.772,.642,0>}
        }
      pigment {
        radial
        color_map {
          [0.0000 color rgbt < 1,0,0,1>]
          [0.1429 color rgbt < 1,0,0,.5>]
          [0.2857 color rgbt < 1,1,0,.5>]
          [0.4286 color rgbt < 0,1,0,.5>]
          [0.5714 color rgbt < 0,1,1,.5>]
          [0.7143 color rgbt < 0,0,1,.5>]
          [0.8571 color rgbt <.5,0,1,.5>]
          [1.0000 color rgbt <.5,0,1,1>]
          }
        frequency 30
        rotate <90,0,-6>
        translate <.06228,0.716595,0>
        }
      finish {ambient 1 diffuse 0}
      }
  
    no_shadow
    no_reflection
    rotate <0,0,5>
    }
      
    difference {  // "Rainbow-colored" beam leaving the droplet
      box {<-10,0,.0002>,<.3,10,.0003> rotate <0,0,38.325> translate <-.827,.557,0>}
      plane {<0,-1,0>,0 rotate <0,0,14.325> translate <-.697,.717,0>}
      cylinder {<0,0,-1>,<0,0,1>,1}
      pigment {
        radial
        color_map {
          [0.0000 color rgbt < 1,0,0,1>]
          [0.1429 color rgbt < 1,0,0,0>]
          [0.2857 color rgbt < 1,1,0,0>]
          [0.4286 color rgbt < 0,1,0,0>]
          [0.5714 color rgbt < 0,1,1,0>]
          [0.7143 color rgbt < 0,0,1,0>]
          [0.8571 color rgbt <.5,0,1,0>]
          [1.0000 color rgbt <.5,0,1,1>]
          }
        frequency 15
        rotate <90,0,-21.3>
        translate <-0.59003,0.744316,0>
        }
      finish {ambient 1 diffuse 0}
      no_shadow
      no_reflection
      }
    
    difference {    // Incoming white light beam
      box {<-100,-1,-.0001>,<0,-.87,.0001>}
      sphere {0,1}
      pigment {
        gradient y
        color_map {
          [0.0 color rgbt<1,1,1,1>]
          [0.2 color rgbt<1,1,1,.9>]
          [0.3 color rgbt<1,1,1,.5>]
          [0.5 color rgbt<1,1,1,0>]
          [0.7 color rgbt<1,1,1,.5>]
          [0.8 color rgbt<1,1,1,1,.9>]
          [1.0 color rgbt<1,1,1,1>]
          }
        scale .13
        translate <0,-1,0>
        }
      finish {
        ambient 1
        diffuse 0
        }
      no_shadow
      no_reflection
      rotate <0,0,-20.825>
      }
          
  #end
  
  difference {  // Droplet - actually a hemisphere for appearance reasons
      sphere {0,1}
      plane {<0,0,1>,.001}
      pigment {color rgbt<.7,.8,1,.7>}
      finish {
          phong 1
          phong_size 80
          reflection .6
          metallic
          }
      }
  
  camera {  // Viewpoint
      up <0,1,0> right <1,0,0>  // Assume square-shaped image format
      location <-.2,0,-2.5>
      look_at <-.2,0,0>
      }
  
  light_source {  // Light
      <-10,0,-10>
      color rgb 1.5
      rotate <0,0,-20.825>
      }

----
POV-Ray "code" for the landscape with rainbows, observer and "droplet cloud":

  /*
  =================================================
  "Landscape" showing the formation of two rainbows
  -------------------------------------------------
  Created by Søren Peo Pedersen - see my user page
  at http://da.wikipedia.org/wiki/Bruger:Peo
  =================================================
  */
  
  plane {   // Flat terrain in the foreground
      <0,1,0>,0
          pigment {color rgb <.65,.7,.6>}
          finish {ambient .4}
          }
  
  plane {<0,0,-1>,0   // Invisible surface carrying the grey "cloud"
      pigment {
          cylindrical
          color_map {
              [0.0 color rgbt<1,1,1,1>]
              [0.5 color rgbt<.7,.7,.7,0>]
              [1.0 color rgbt<.5,.5,.5,0>]
              }        
          rotate <90,0,0>
          scale 7
          translate <8,8,0>
          turbulence .3
          }
      finish {ambient 1 diffuse 0}
      }
  
  sky_sphere {        // Provides a sky with light blue color gradient
      pigment {
          gradient y
          color_map {
              [0 color rgb <.1,.3,.2>]
              [.5 color rgb <.65,.7,.6>]
              [.5 color rgb <.8,.9,1>]
              [1 color rgb <.2,.5,1>]
              }
          translate -.5
          scale 2
          turbulence .1
          }
      }
  
  union { // The observer in the lower, left-hand corner
      sphere {0,1 scale <.2,.8,.2> pigment {color rgb <0,0,1>} finish {ambient .5}}
      sphere {<0,1,0>,.2 pigment {color rgb <1,.7,.4>} finish {ambient .5}}
      translate <-6.5,0,-4>
      }
  
  #macro ColorFunction(Plads)   // Creates a color from the spectrum (from 0=red to 1=purple)
      #local U=4.9999*(Plads-int(Plads*4.9999)/4.9999);
      #switch (Plads)
      #range (0.0,0.2) color rgb < 1 , U , 0 > #break
      #range (0.2,0.4) color rgb <1-U, 1 , 0 > #break
      #range (0.4,0.6) color rgb < 0 , 1 , U > #break
      #range (0.6,0.8) color rgb < 0 ,1-U, 1 > #break
      #range (0.8,1.0) color rgb < U , 0 , 1 > #break
      #end
  #end
  
  #macro Beam(Num,Primay)   // Renders a white incoming beam, and a colored "returned" beam
      #local R=seed(145*Num);
      #local Lgd=11+rand(R)*3;
      #if (Primay)
          #local Vinkel=42.3-20.825-1.7*Num;
      #else
          #local Vinkel=50.7-20.825+2.9*Num;
      #end
      merge {
          cylinder {0,<Lgd,0,0>,.01
              pigment {ColorFunction(Num)}
              finish {ambient 1 diffuse 0}
              rotate <0,0,Vinkel>
              translate <-6.5,1,-4>
              no_shadow
              }
          cylinder {
              <-100,0,0>,0,.01
              rotate <0,0,-20.825>
              translate <-6.5+Lgd*cos(radians(Vinkel)),1+Lgd*sin(radians(Vinkel)),-4>}
              pigment {color rgb 1}
              finish {ambient 1 diffuse 0}
          }
  #end
  
  // Light beams forming the primary rainbow:
  #object {Beam(0.00,yes)}
  #object {Beam(0.25,yes)}
  #object {Beam(0.50,yes)}
  #object {Beam(0.75,yes)}
  #object {Beam(1.00,yes)}
  
  // Light beams forming the secondary rainbow:
  #object {Beam(0.00,no)}
  #object {Beam(0.25,no)}
  #object {Beam(0.50,no)}
  #object {Beam(0.75,no)}
  #object {Beam(1.00,no)}
  
  // Totally transparent pigment set of primary and secondary arc
  #local ArcPgmt0=pigment {
      cylindrical
      color_map {
          [0.0 color rgbt<1,1,1,1>]
          [0.00001 color rgbt<1,0,1,1>]
          [0.022   color rgbt<0,0,1,1>]
          [0.044   color rgbt<0,1,1,1>]
          [0.066   color rgbt<0,1,0,1>]
          [0.088   color rgbt<1,1,0,1>]
          [0.11 color rgbt<1,0,0,1>]
          [0.11 color rgbt<1,1,1,1>]
          [0.39 color rgbt<1,1,1,1>]
          [0.39 color rgbt<1,0,0,1>]
          [0.40 color rgbt<1,1,0,1>]
          [0.41 color rgbt<0,1,0,1>]
          [0.42 color rgbt<0,1,1,1>]
          [0.43 color rgbt<0,0,1,1>]
          [0.44 color rgbt<1,0,1,1>]
          [0.44 color rgbt<1,1,1,1>]
          [1.0 color rgbt<1,1,1,1>]
          }    
      }
  
  // Slightly non-transparent pigment set of primary and secondary arc
  #local ArcPgmt1=pigment {
      cylindrical
      color_map {
          [0.0 color rgbt<1,1,1,1>]
          [0.00001 color rgbt<1,0,1,.7>]
          [0.022   color rgbt<0,0,1,.7>]
          [0.044   color rgbt<0,1,1,.7>]
          [0.066   color rgbt<0,1,0,.7>]
          [0.088   color rgbt<1,1,0,.7>]
          [0.11 color rgbt<1,0,0,0>]
          [0.11 color rgbt<1,1,1,1>]
          [0.39 color rgbt<1,1,1,1>]
          [0.39 color rgbt<1,0,0,.2>]
          [0.40 color rgbt<1,1,0,.2>]
          [0.41 color rgbt<0,1,0,.2>]
          [0.42 color rgbt<0,1,1,.2>]
          [0.43 color rgbt<0,0,1,.2>]
          [0.44 color rgbt<1,0,1,.2>]
          [0.44 color rgbt<1,1,1,1>]
          [1.0 color rgbt<1,1,1,1>]
          }    
      }
  
  // Surface carrying the two rainbows in front of the grey "cloud"
  plane {<-1,0,0>,0
      pigment {
          radial
          pigment_map {
              [0.0 ArcPgmt1]
              [0.2 ArcPgmt0]
              [0.8 ArcPgmt0]
              [1.0 ArcPgmt1]
              }        
          rotate <0,0,90>
          scale <4.18495,4.18495,7>
          translate <0,1,-4>
          }
      finish {ambient 1 diffuse 0}
      hollow
      no_shadow
      }
  
  // Viewpoint
  camera {
      location <-5,5,-15>
      look_at <1,4,0>
      }
  
  // "Infinitely" remote light source with parallel rays:
  light_source {
      <-1000,0,0>    
      color rgb 1.5
      rotate <0,0,-20.825>
      parallel
      }