Donald, Thank you for the conical explaination and the exact radius dimenstions. I'm glad to hear that my interpretation of the event was correct. The important point which you mentioned with the good example of two people standing next to each other is that a rainbow moves with the observer. I learned this as a kid on long country car rides seeing that the rainbow stayed in the same place with respect to my eyes yet the car was constantly moving. It was easy to see that the rainbow was moving along with me.
John >Hello Jim, >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 ><!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> ><HTML><HEAD> ><META content="text/html; charset=iso-8859-1" http-equiv=Content-Type> ><META content="MSHTML 5.00.3019.2500" name=GENERATOR> ><STYLE></STYLE> ></HEAD> ><BODY bgColor=#ffffff> ><DIV><FONT size=2> ><DIV><FONT size=2>Hello Jim,</FONT></DIV> ><DIV><FONT size=2>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.</FONT></DIV> ><DIV> </DIV> ><DIV><FONT size=2> Don >Snyder</FONT></DIV> ><DIV></FONT>----- Original Message ----- </DIV></DIV> ><BLOCKQUOTE >style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px"> > <DIV > style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> > <A href="mailto:[EMAIL PROTECTED]" > [EMAIL PROTECTED]>J.Tallman</A> </DIV> > <DIV style="FONT: 10pt arial"><B>To:</B> <A > href="mailto:sundial@rrz.uni-koeln.de"; [EMAIL PROTECTED]>Sundial > List</A> ; <A href="mailto:[EMAIL PROTECTED]" > [EMAIL PROTECTED]>John Carmichael</A> </DIV> > <DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, January 11, 2001 8:50 > AM</DIV> > <DIV style="FONT: 10pt arial"><B>Subject:</B> Rainbow geometry</DIV> > <DIV><BR></DIV> > <DIV><FONT size=2>Hello All,</FONT></DIV> > <DIV><FONT size=2></FONT> </DIV> > <DIV><FONT size=2>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 <EM>was</EM> > the pot that day.</FONT></DIV> > <DIV><FONT size=2></FONT> </DIV> > <DIV><FONT size=2>Does anyone know the determining factor for the radius of a > rainbow?</FONT></DIV> > <DIV><FONT size=2></FONT> </DIV> > <DIV><FONT size=2>Jim Tallman</FONT></DIV> > <DIV><FONT size=2>Sr. Designer</FONT></DIV> > <DIV><FONT size=2>FX Studios</FONT></DIV></BLOCKQUOTE></BODY></HTML> >
