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 Post subject: How do you find the maximum angle for reflection?
PostPosted: Tue Dec 19, 2017 2:56 pm 
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Location: Tampa, Florida
OK guys I have tried for the past hour to figure this problem out but it literally feels like I'm trying to understand an alien language that appears to be as complicated and difficult to understand as humanly possible.

We all know the common literature for critical angles. It's easy to find out that the critical angle for Tourmaline is 38.12- which is the minimum angle for reflection to occur.

Now when I try to find the answer to what the maximum angle is for reflection I get absolutely nothing but Snell's law which I am really lost on using at this point.

My question is, if the minimum angle is 38.12 what is the maximum angle? What is the angle that light will not reflect back to the viewer? From experience I know it's around 60 degrees... How can I calculate it with mathematics? I remember seeing some information somewhere but I can't find it for the life of me.

The reason I am wondering this is I'm designing for closed-C Tourmaline and want to know how steep I have to make the ends for the dark not to show up. A lot of stones I have to recut are damn near 90 degrees on the ends and I want to make them the most professional I can. From what I'm imagining the steeper the better, but what can I get away with if it is cut improperly? What angle should I choose to cut away an angle that is showing the dark of the C-axis? 60 or 65 degrees?

Thank you for your help!


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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Tue Dec 19, 2017 5:40 pm 
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Here is the link to a Java-based tutorial on refraction from Florida State University:
https://www.olympus-lifescience.com/en/ ... ionangles/
Here is a mathematical tutorial on both refraction and reflection which may answer your question:
http://rmico.com/reflection-and-refract ... t-tutorial

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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Wed Dec 20, 2017 10:22 am 
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Joined: Sat Apr 24, 2010 7:10 am
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easy it will reflect all the way to zero


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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Thu Dec 21, 2017 12:03 pm 
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Joined: Thu Jun 03, 2010 1:49 pm
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Location: South Africa
I remember an article which dealt with the maximum angle, it was to do with emeralds and was very thorough. I remember that for quartz it was either side of 50 degrees, surprisingly low.

For closed c tourmaline the 2 designs I have from 2 authors use 63 and 70 degrees.
For the mathematics I think the links posted by Thomas will get you there.

Good luck, I gave up with closed c long ago.


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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Thu Dec 21, 2017 12:26 pm 
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Joined: Thu Jun 03, 2010 1:49 pm
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Location: South Africa
http://www.ruby-sapphire.com/brilliance_windows_extinction.htm

This may be a starting point.


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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Thu Dec 21, 2017 2:37 pm 
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For a simple prism the math is not too problematic (for simple light from above), it's a geometry problem more than a Snell's law problem.

The low is the critical angle of the material (CA), and the high is 60-CA/3, so for Tourmaline thats 38.1 - 47.3. But that's a simple prism model with no crown tier, and collimated light from above.

The 'best' (mathematically) wiggle room for tilt still producing light return (same simple model) is 30+CA/3 (which is 43.5 for Quartz, 41.5 for Corundum, etc.)

Again, all for a simple cone prism, not for actual stone designs where there are multiple tiers, or more complex lighting models. I use this framework as a starting point, real stones usually have more room because on the high side due to the extra tiers etc.


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 Post subject: Re: How do you find the maximum angle for reflection?
PostPosted: Fri Dec 22, 2017 12:06 pm 
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Joined: Thu Jun 03, 2010 1:49 pm
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No response from the OP. Must have found a solution.

Contemplating the problem, really the mathematics is irrelevant, the axis is closed. So now it's just to get to an angle that can actually work in a setting. I would start at 70 degrees, it's easier to go down a little if you have to.
Pavilion is best left as a step cut, the other options I've seen all result in some degree of extinction.
The crown ends also need to be steep.
The corners must be as small as practical, IE : no ECED otherwise the ends are darker than necessary.
The stone needs to be as long as practical, the closer to 1/1 ratio you get the worse the stone will perform.

Prepare to be disappointed often.


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