Imagen:Prisms with high and low dispersion.png

Two pictures of optical prisms; one (above) with a high degree of optical dispersion, and one (below) with a low dispersion. For each image, a different setting of the "Disp" variable in the code below to have each image show a different amount of optical dispersion.

Simulated using computer graphics, rendered using the Persistence of Vision Raytracer. Everything made from scratch by Peo, originally for use in a few articles in danish Wikipedia.

I, the author of this work, hereby publish it under the following license: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". العربية | Česky | Deutsch | English | Español | Français | Italiano | 日本語 | 한국어 | Nederlands | Polski | Português | Slovenčina | Svenska | עברית +/-

The code below was used to render each prism, and the two images was subsequently merged into this image in a photomanipulation application.

global_settings {
    max_trace_level 64
    max_intersections 1000
}

// "Disp" variable: Amount of dispersion: Looks reasonable 
// from 2 (less) thru 6 (more dispersion), including both:
#declare Disp=6;

light_source {<-100,50,-30> color rgb .3}
light_source {<-150,120,-100> color rgb .3}

camera {
    location <-4,5,-9>
    look_at <3,-2,0>    
    angle 60    
    }

#local L1a = tan(Disp/180*pi);
#local L1b = 1.05+L1a*1.13;

#local L2a = -tan(Disp/180*pi);
#local L2b = .739+L2a*1.308;

#local SPLx = (L2b-L1b)/(L1a-L2a);  // Center of radial rainbow pattern in the part of
#local SPLy = L1a*SPLx+L1b;         // the light beam that's inside the prism.

#local TOPx = (3-L1b)/(L1a+1.73205087569);
#local TOPy = L1a*TOPx+L1b;

#local BOTx = (3-L2b)/(L2a+1.73205087569);
#local BOTy = L2a*BOTx+L2b;

#local TOPa = tan(radians(2*Disp-30));
#local TOPb = TOPy-TOPa*TOPx;

#local BOTa = tan(radians(-2*Disp-30));
#local BOTb = BOTy-BOTa*BOTx;

#local OUTx = (BOTb-TOPb)/(TOPa-BOTa);
#local OUTy = BOTa*OUTx+BOTb;

#local txtOff=texture {pigment {color rgb 1}} // Texture for unlit walls

#local txtFLT=texture {pigment {  // Radial pattern to fake the "rainbow-
        radial                    // illuminated" part of the wall and floor.
        color_map {
            [0.00 color rgb <.7,(1-Disp/10),1>]           // Colors vary from all white
            [0.20 color rgb <(1-Disp/10),(1-Disp/10),1>]  // to the rainbow of saturated
            [0.40 color rgb <(1-Disp/10),1,1>]            // colors, depending on "Disp"
            [0.60 color rgb <(1-Disp/10),1,(1-Disp/10)>]  // setting.
            [0.80 color rgb <1,1,(1-Disp/10)>]
            [1.00 color rgb <1,(1-Disp/10),(1-Disp/10)>]
            }                                                  
        frequency int(90/Disp+.5) // Agular width - causes discrete intervals in width!
    } finish {ambient .4}}

#local txtSTR=texture { // This texture encloses the above, "ranbow-illuminated"
    radial              // texture with zones at the red and purple ends where the
    texture_map {       // rainbow "fades out" into the invisible, and thus appa-
        [0.00 txtOff]   // rently unlit parts of the floor and walls.
        [0.01 txtFLT]
        [Disp/90-.01 txtFLT]
        [Disp/90 txtOff]
        [1.00 txtOff]
        }
    rotate <90,0,-30-2*Disp>
    translate <OUTx,OUTy,0>
    }

union {   // The floor and walls in the scenery:
    plane {<0,1,0>,-3.001}  // Floor
    plane {<-1,0,0>,-10}    // Wall struck by colored light
    plane {<0,0,-1>,-15}    // Unlit wall in the background
    texture {               // This texture is the rainbow band in txtSTR inside a
        gradient z          // small strip along the triangular surfaces of the
        texture_map {       // prism, surrounded by zones where the light fades out
            [0.000 txtOff]  // into the dark gray, "unlit" texture.
            [0.004 txtSTR]
            [0.016 txtSTR]
            [0.020 txtOff]
            [1.000 txtOff]
            }
        translate <0,0,-.01>
        scale <1,1,200>
        }
    }    

difference {  // The prism itself
    box {<-10,-3,-2>,<10,3,2>}              // Shape made from a box, "cut" into
    plane {<0,-1,0>,-1.5 rotate <0,0,60>}   // shape using two planes at 60* angles.
    plane {<0,-1,0>,-1.5 rotate <0,0,-60>}
    hollow on                                 // Media stuff: The prism has an index
    pigment {color rgbt <.8,1,.9,.7>}         // of refraction (ior) of 1.66, and
    finish {phong 1 reflection .1 ambient .3} // disperses colors according to the
    interior {ior 1.66 dispersion 1+Disp/100} // "Disp" variable.
    }

difference {  // The narrow "sheet" of white light entering the prism from the left:
    box {<-10,-.1,-1.5>,<1,.1,1.5> rotate <0,0,26.099> translate <-1,1,0>}
    plane {<0,1,0>,1.5001 rotate <0,0,60>}  // Box "cut" into shape with a plane.
    hollow on               // Media stuff: The beam shape itself is invisible, but
    pigment {color rgbt 1}  // contains an emitting media, giving the beam the
    interior {              // "fuzzy", translucent look.
        media {
            intervals 10  samples 1,1  confidence 0.9  variance 1.0/128
            ratio 0.9  emission rgb .6  method 3
            }
        }
    }

difference {    // Part of the light beam inside the prism:
    box {<-2,-2,-1.5>,<5,2,1.5>}                                    // Box cut to shape
    plane {<0,-1,0>,0 rotate <0,0,Disp> translate <-1.13,1.05,0>}   // with planes, ac-
    plane {<0,1,0>,0 rotate <0,0,-Disp> translate <-1.308,0.739,0>} // cording to the
    plane {<0,-1,0>,-1.499 rotate <0,0,60>}                         // "Disp" variable
    plane {<0,-1,0>,-1.499 rotate <0,0,-60>}
    hollow on                       // Media stuff: The shape itself is invisible inside
    pigment {color rgbt <1,1,1,1>}  // the prism since it has the same ior; 1.66
    finish {ambient .7}
    interior {
        ior 1.66 dispersion 1+Disp/100
        media {
            intervals 10        // number of intervals used for sampling [10]
            samples 1,1         // minimum and maximum number of samples taken per interval [1,1]
            confidence 0.9      // statistic parameter higher->better quality [0.9]
            variance 1.0/128    // statistic parameter lower->better quality [1.0/128]
            ratio 0.9           // distribution between lit and unlit areas [0.9]
            emission rgb<1,.95,.85>*.4
            method 3               // adaptive sampling
            density {
                radial
                color_map { // Color spectrum in the beam inside the prism:
                    [0.00 color rgb <1,(1-Disp/10),(1-Disp/10)>*(1.5-.05*Disp)]
                    [0.20 color rgb <1,1,(1-Disp/10)>          *(1.5-.05*Disp)]
                    [0.40 color rgb <(1-Disp/10),1,(1-Disp/10)>*(1.5-.05*Disp)]
                    [0.60 color rgb <(1-Disp/10),1,1>          *(1.5-.05*Disp)]
                    [0.80 color rgb <(1-Disp/10),(1-Disp/10),1>*(1.5-.05*Disp)]
                    [1.00 color rgb <1,(1-Disp/10),1>          *(1.5-.05*Disp)]
                    }
                frequency int(180/Disp+.5)
                rotate <-90,0,-Disp>
                translate <SPLx,SPLy,0>
                }
            }
        }
    }

difference {  // Part of the light beam exiting at the right-hand side of the prism:
    box {<-5,-500,-1.5>,<500,5,1.5>}                                  // Box cut to sha-
    plane {<0,1,0>,1.5001 rotate <0,0,-60>}                           // pe using three
    plane {<0,-1,0>,0 rotate <0,0,2*Disp-30> translate <TOPx,TOPy,0>} // planes.
    plane {<0,1,0>,0 rotate <0,0,-2*Disp-30> translate <BOTx,BOTy,0>}
    hollow on                       // Media stuff: Like the entering beam, this one's
    pigment {color rgbt <1,1,1,1>}  // shape is invisible, but contains emitting media
    finish {ambient .7}             // showing the rainbow "band" of colors
    interior {        
        media {
            intervals 10  samples 1,1  confidence 0.9  variance 1.0/128
            ratio 0.9  emission rgb<1,.95,.85>*.4  method 3
            density {
                radial
                color_map { // Color spectrum in the beam leaving the prism:
                    [0.00 color rgb <1,(1-Disp/10),(1-Disp/10)>*(.4-.01*Disp)]
                    [0.20 color rgb <1,1,(1-Disp/10)>          *(.4-.01*Disp)]
                    [0.40 color rgb <(1-Disp/10),1,(1-Disp/10)>*(.4-.01*Disp)]
                    [0.60 color rgb <(1-Disp/10),1,1>          *(.4-.01*Disp)]
                    [0.80 color rgb <(1-Disp/10),(1-Disp/10),1>*(.4-.01*Disp)]
                    [1.00 color rgb <.7,(1-Disp/10),1>          *(.4-.01*Disp)]
                    }                                                  
                frequency int(90/Disp+.5)
                rotate <-90,0,-30-2*Disp>
                translate <OUTx,OUTy,0>
                }
            }
        }
    }