----- Original Message -----
From: "Tom Miller" <tomwmil...@attbi.com>
To: <pinhole-discussion@p at ???????>

> I've read a rule
> of thumb that at 30 degrees the fall of is one stop and that at 45 degrees
> it is two stops.  It seems like there is a possibly handy formula in
there.

Tom,

Forgot answering this other question.

That rule of thumb is good, but to be precise, 1 stop is at 32.76 degrees.

A formula to find the angle at which a specific fall off is found would be:

If  S = stops of fall off

Angle = ArcCosine [(1 / 2^S)^0.25]  or for better clarity:
http://members.rogers.com/gpenate/angle.gif

for 1 stops it would be:

Angle = ArcCosine [(1 / 2^1)^0.25]
Angle = ArcCosine [(1 / 2)^0.25]
Angle = ArcCosine [0.5^0.25]
Angle = ArcCosine [0.840896]
Angle = 32.76 degrees

for 2 stops it would be:

Angle = ArcCosine [(1 / 2^2)^0.25]
Angle = ArcCosine [(1 / 4)^0.25]
Angle = ArcCosine [0.25^0.25]
Angle = ArcCosine [0.70710678]
Angle = 45 degrees

Guillermo


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