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   Secondary Bow Formation 
    

 
Light emerging after two internal reflections forms the secondary bow. Light reflected more than twice goes into higher order bows.
 
  Two internal reflections.
   
  Mouse over the slider to see the ray paths. Compare them with those of the primary bow, shown faintly here and more completely in the primary ray diagram.
    
  Many different ray paths
  Secondary bow rays* are deviated** through more than 180º. There is a minimum deviation of about 231º corresponding to the inner edge of the secondary bow. Its radius is therefore 231 - 180 = 51º. Rays cluster around the minimum deviation condition to form the brightest part of the bow.
  
  Minimum deviation angle
The minimum deviation rays enter much closer to the drop's edge than the corresponding rays of the primary bow.
 
Closer to the drop edge
Why are the secondary colours reversed? Red light is refracted least and so its rays suffer the smallest deviation. But the total deviation is more than 180º and the least deviated rays appear at the inside of the bow.
   
Colour reversal
  No light from secondary rays appears at less than 51º from the center and no light from the primary appears more than than 42º. The sky between is dark (but not quite, see the 5th order bow). This is Alexanders dark band.
   
 
  Inside the bow is dark
  Ray paths are a good approximation to how light behaves when the raindrops are several millimetres across. Smaller drops require a treatment which takes account of the wave nature of light.
  
  Don't take ray paths too seriously
  **  Deviations are traditionally measured from the direction of the incoming sunlight.
   
  Deviation angles
  ***  The ray paths are accurately computed for wavelengths of 400 and 750 nm passing through a water drop at 0 Celsius.
  
  Calculation









Secondary bow rays.

There are two internal reflections and rays are deviated more than 180º. The 51° radius bow occurs at the minimum deviation angle of 231°.