to write the final formula
G = 4 * sin-1( H / n) - 2 * sin-1( H ) If you plot this for water (n = 1.333) you get the graph below. H = ( (4 - n2) / 3 )1/2 And therefore, G has a maximum value given by
Using n for water of 1.333 you get
You can also see that from the graph above. Now you see why it is that
if you stand with your back to the sun so you are facing the same direction
as the incoming sunlight, you need to look at an angle of 42.0 degrees
to see the rainbow. Also note that this maxima in
G(H) means that
all of the light that enters at near this height comes out at essentially
the same angle and so you get more light at this angle than any other.
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