Actually, if my physics recollection is correct, the light rays (or shadows) bend twice for each pane. Once on entry, "towards" the glass (denser medium), then again on exit, paralleling the entering ray (assuming same density medium on both sides of the glass). This introduces an offset whose magnitude depends upon the angle of entry. If the ray enters normal to the glass, there is no deviation. If at a very shallow angle, a large deviation.
The same thing happens as the ray progresses through the second pane. Thicker glass introduces a greater offset, since the ray travels farther at the angle within the glass. Greater distance between the panes only adds to the initial distance between the style and the dial plane. Note that the angle of the ray within the glass is less (measured with respect to the normal) than in air. This tells me the direction of the offset is such that it slightly negates the offset due to the distance from style to dial. Dave Sent from my iPhone On Aug 4, 2011, at 4:36 PM, "John Carmichael" <[email protected]> wrote: > Karon: > > > > This I know to be true: Most window glass all have the same standard > thickness of 1/8”. Large and small windows all use the same glass as far as > thickness goes. Also, when double panes are used, they usually put the same > air gap in all window sizes too. So the glass is the same and the air gap is > the same for all sized windows. > > > > The bending of the light ray only occurs when the shadow hits the outer > glass, so the distance between the nodus and the glass doesn’t affect the > refraction. So I’m thinking the light will bend the same when it hit the > outer glass on big and small windows. > > > > Since the hour and date lines are much closer on small dials, the time and > date readings would be bigger on a small window. > > > > Let’s wait to see what Fer says (Fer is one of the smartest guys on our list). > > > > John > > > > From: karon [mailto:[email protected]] > Sent: Thursday, August 04, 2011 4:15 PM > To: 'John Carmichael'; 'fer de vries'; [email protected] > Subject: RE: mock stained glass sundial > > > > But, John, if you have a larger window, the glass is thicker and the space > between both panes would be more, wouldn’t it? that means not only is your > refraction error larger but, since your angles arcs take up more space, the > error is easier to perceive. > > > > Even if you have more error on a smaller piece, you would be less likely to > notice it since the arc distance is so small. The larger and, therefore, more > potentially accurate a sundial is, the more obvious any error would be. > > > > > > Karon Adams > > Accredited Jewelry Professional (GIA) > > You can send a free Rosary to a soldier! > > www.facebook.com/MilitaryRosary > > www.YellowRibbonRosaries.com > > > > From: [email protected] [mailto:[email protected]] On > Behalf Of John Carmichael > Sent: Thursday, August 04, 2011 7:04 PM > To: 'fer de vries'; [email protected] > Subject: RE: mock stained glass sundial > > > > Hi Fer: > > > > Your answer got me to thinking! > > > > It seems to me that the total size of the glass sundial face would have a > huge impact on how significant the double glass refraction error is. I’m > thinking that the bigger the sundial face, the less significant the > refraction error would be. > > > > Follow my thinking in these two examples: > > > > Let’s say you have two faux stained glass sundials painted on the inner panes > of glass, and both sundials have the same small air gap between the inner and > outer panes. But one sundial is ten times bigger than the other sundial. > Wouldn’t the amount of refraction be the same for both sundials since the air > gap and the glass thickness is the same on each? If so, then the hour and > date line error shift would be a lot smaller on the the big dial. > > > > Or to put it a different way- > > If the refraction shifts the shadow 1 cm, that would be less of an error on a > big dial face than on a small dial face. > > > > Is my thinking wrong? > > > > Thx > > > > John > > > > p.s. > > > > From: fer de vries [mailto:[email protected]] > Sent: Thursday, August 04, 2011 10:00 AM > To: John Carmichael; [email protected] > Subject: Re: mock stained glass sundial > > > > Hi John, > > > > I had to walk my room a number of times to know the answer but I think I do > now. > > > > The glass panes add an error in the reading of the dial. > > As long as you don't change the thickness of the panes the x,y shift of a > certain point is constant in values. > > > > Increasing the distance between the panes enlarges the dimensions of the > sundial pattern. > > So relative the x/y shift has less effect on the reading and the error > decreases. > > > > The same happens if you enlarge the distance from the outside pane to the > index on the gnomon. > > Then also the dials dimensions increase and the error decreases. > > > > > > This is also an answer to Karons question about changing the thicknes of the > glass panes. > > Then the x/y shift increases in values and an extra error is aded. > > > > > > Best wishes, Fer. > > > > Fer J. de Vries > > > > De Zonnewijzerkring > http://www.de-zonnewijzerkring.nl > > > > Molens > http://www.collsemolen.dse.nl > > > > Eindhoven, Netherlands > lat. 51:30 N long. 5:30 E > > ----- Original Message ----- > > From: John Carmichael > > To: [email protected] > > Sent: Thursday, August 04, 2011 4:13 PM > > Subject: RE: mock stained glass sundial > > > > Thanks for checking on that Fer, making a drawing, and for correction my > assumption. You taught me not to assume anything! > > > > I have a question though- > > > > Does the refraction error increase if the distance between the two glass > panes increases? > > > > From: fer de vries [mailto:[email protected]] > Sent: Thursday, August 04, 2011 1:29 AM > To: Mike Shaw; [email protected]; 'John Carmichael'; [email protected] > Subject: Re: mock stained glass sundial > > > > Mike, > > > > Your question: > > ***** > > If you are going to allow your shadow to pass through two panes of glass, > will refraction start to become important? > > ***** > > > > John Carmicael answered: > > ***** > > It's insignificant. > > ***** > > > > My answer is: > > It is significant. > > > > Your statement is: .... shadow to pass through two panes of glass .... > > This means that the gnomon is at the outside of the double glass and the > sundials pattern is at the inside of the double glass. > > > > As an example I calculated such a vertical south facing dial for latitude 45 > degrees with hourlines and datelines. > > The double glass has panes of 5 mm and the space between is 15 mm. Rather > normal values. > > The glass has a refraction index of 1.4 > > For the index for the datelines I have chosen a distance from the glass of 20 > mm. > > I assume the refraction index of the space between the panes is 1. (No > refraction). > > > > The pattern of the sundial is attached and shows a significant shift, > especially for the datelines. > > (It is only 16 kB and should pass.) > > > > Black lines are without refraction, blue lines with refraction. > > > > Best wishes, Fer. > > > > > > Fer J. de Vries > > > > De Zonnewijzerkring > http://www.de-zonnewijzerkring.nl > > > > Molens > http://www.collsemolen.dse.nl > > > > Eindhoven, Netherlands > lat. 51:30 N long. 5:30 E > > ----- Original Message ----- > > From: Mike Shaw > > To: [email protected] ; 'John Carmichael' ; [email protected] > > Sent: Wednesday, August 03, 2011 5:28 PM > > Subject: Re: mock stained glass sundial > > > > If you are going to allow your shadow to pass through two panes of glass, > will refraction start to become important? > > > > Mike Shaw > 53º 22'N 03º02'W > www.wiz.to/sundials > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial >
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