Re: Rainbow geometry

[Donald L. Snyder]

Hello Jim and maybe all, This is my first attempt at sending a note to "all", so please excuse me if you get two copies or some other unpredictable outcome............   I happen to have a book on my shelf by Robert Greenler titled "Rainbows, Halos, and Glories."  In the first few pages of the book, he discusses the "size" of a rainbow.  Evidently, the theory about the size is due to Descarte in 1637.  Rainbows are circular. Imagine a line extending from the center of the rainbow back towards the observer and hence towards the sun.  The half angle of the cone subtended by the rainbow with apex at the observer is 42 degrees; i.e., this is the angle from the axis of the cone to the cone's edge.  As has been mentioned in the discussion, some of the rainbow's circle may be below the horizon and not visible.  Also, a fainter, secondary rainbow can appear at 51 degrees.  To return to your question, the radius of the rainbow will depend on the distance, D, from the observer to the water droplets causing the rainbow.  Hence, the radius can be predicted as R = D*tan(42), but the distance must be known.  You will know this when you keep track of how far you travel to retrieve the pot at the end of the rainbow, assuming that part of the rainbow is below the horizon so there is an end.  Another comment made by Greenler is that a typical lens on a 35mm camera has a field of view of around 40 degrees, making it difficult to photograph a rainbow with such a lens whether the rainbow results from the spray of a garden hose you're holding or from a distant rainstorm.  Also, two people standing side by side and observing a rainbow are actually looking at different sets of water droplets, so each has a personal rainbow.  Hopefully, the times they deduce from the individual rainbows will be identical.             Don Snyder ----- Original Message ----- From: J.Tallman To: Sundial List ; John Carmichael Sent: Thursday, January 11, 2001 8:50 AM Subject: Rainbow geometry Hello All,   What a fascinating observation on the practical aspects of a rainbow...thanks for the commentary John.  I have always been interested in rainbows, ever since my third grade teacher took the whole class out trudging through the fields after a rainstorm, looking for the pot at the end of the rainbow.  We never found it...maybe the rainbow was the pot that day.   Does anyone know the determining factor for the radius of a rainbow?   Jim Tallman Sr. Designer FX Studios