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File:Rainbow formation.png

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Descrizione
English: Diagram showing how primary and secondary rainbows are formed due to the light propagation in spherical droplets. Details follow soon!

Legend:

  1. Spherical droplet
  2. Places where internal reflection of the light occurs
  3. Primary rainbow
  4. Places where refraction of the light occurs
  5. Secondary rainbow
  6. Incoming beams of white light
  7. Path of light contributing to primary rainbow
  8. Path of light contributing to secondary rainbow
  9. Observer
  10. Region forming the primary rainbow
  11. Region forming the secondary raimbow
  12. Zone in the atmosphere holding countless tiny spherical droplets
Español: Diagrama que muestra como se forman los arco iris primarios y secundarios debido a la descomposición de luz blanca en gotitas esféricas:

Leyenda:

  1. Gotitas esféricas
  2. Lugares donde ocurre el reflejo interno de la luz
  3. Arco iris primario
  4. Lugares donde ocurre la refracción de la luz.
  5. Arco iris secundario
  6. Rayos entrantes de luz blanca
  7. Recorrido de la luz que forma el arco iris primario
  8. Recorrido de la luz que forma el arco iris secundario
  9. Observador
  10. Región que forma el arco iris primario
  11. Región que forma el arco iris secundario
  12. Zona en la atmósfera llena de incontables diminutas gotitas esféricas
Português: Diagrama que mostra como se formam os arco-íris primários e secundários em função da decomposição de luz branca em gotículas esféricas:

Legenda:

  1. Gotículas esféricas;
  2. Locais onde ocorre o reflexo interno da luz;
  3. Arco-íris primário;
  4. Locais onde ocorre a refração da luz;
  5. Arco-íris secundário;
  6. Raios incidentes de luz branca;
  7. Caminho percorrido pelo luz que forma o arco-íris primário;
  8. Caminho percorrido pelo luz que forma o arco-íris secundário;
  9. Observador;
  10. Região que forma o arco-íris primário;
  11. Região que forma o arco-íris secundário;
  12. Zona na atmosfera plena de incontáveis e diminutas gotículas esféricas.
Català: Diagrama que mostra com es formen els arcs de Sant Martí primaris i secundaris a causa de la descomposició de la llum blanca en gotes esfèriques:

Llegenda:

  1. Gotes esfèriques
  2. Punts on succeeix el reflex intern de la llum
  3. Arc de Sant Martí primari
  4. Llocs on succeeix la refracció atmosfèrica.
  5. Arc de Sant Martí secundari
  6. Raigs entrants de llum blanca
  7. Recorregut de la llum que forma l'arc de Sant Martí primari
  8. Recorregut de la llum que forma l'arc de Sant Martí secundari
  9. Observador
  10. Regió que forma l'arc de Sant Martí primari
  11. Regió que forma l'arc de Sant Martí secundari
  12. Zona de l'atmosfera plena de petites gotes esfèriques
Tiếng Việt: Sơ đồ cho thấy cách cầu vồng sơ cấp và thứ cấp được hình thành do sự truyền ánh sáng trong các giọt hình cầu. Thông tin chi tiết theo dõi ngay sau đây:

Huyền thoại:

  1. Giọt hình cầu
  2. Những nơi xảy ra phản xạ bên trong của ánh sáng
  3. Cầu vồng chính
  4. Những nơi xảy ra hiện tượng khúc xạ ánh sáng
  5. Cầu vồng phụ
  6. Chùm ánh sáng trắng tới
  7. Đường đi của ánh sáng góp phần tạo nên cầu vồng chính
  8. Đường đi của ánh sáng góp phần tạo nên cầu vồng thứ cấp
  9. Người quan sát
  10. Vùng hình thành cầu vồng chính
  11. Khu vực hình thành cầu vồng thứ cấp
  12. Vùng trong bầu khí quyển chứa vô số giọt hình cầu nhỏ
Fonte See below / Mirar abajo / Ver abaixo
Autore Peo
Io, detentore del copyright su quest'opera, dichiaro di pubblicarla con le seguenti licenze:
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Español: Tres imágenes trazadas de rayos, creadas usando POV-Ray, puestas juntas y añadidos después números y líneas negras en un paquete de software de gráficos. Abajo se encuentra el "código" para crear los diagramas de arriba, y el paisaje de abajo respectivamente:
English: Three raytraced images, created using POV-Ray (see http://www.povray.org/), put together and numbers and black lines added in a graphics software package afterwards. Below is the "code" to create the diagrams above, and the landscape below, respectively:
Tiếng Việt: Ba hình ảnh raytraced, được tạo bằng POV-Ray (xem http://www.povray.org/), được ghép lại với nhau và các số và dòng màu đen được thêm vào trong một gói phần mềm đồ họa sau đó. Dưới đây là "mã" để tạo các sơ đồ ở trên và cảnh quan bên dưới, tương ứng:

POV-Ray "code" for the diagrams showing light propagation inside the droplets: 

  /*
  =================================================
  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
      }

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attuale13:56, 9 apr 2005Miniatura della versione delle 13:56, 9 apr 2005721 × 902 (280 KB)Peo~commonswikiDiagram showing how primary and secondary rainbows are formed. Details follow soon! {{GFDL-self}}

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Estratto da "https://it.wikipedia.org/wiki/File:Rainbow_formation.png"