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Calculating sagitta of a convex lens

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#1 David Dakstar

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Posted 24 May 2024 - 07:08 AM

I would like to make a  Schupman telescope. The objective is a double convex lens. 4 inches in diameter. R1 radius is 27.133 inches, R2 radius is 302.400 inches. I have never made a lens and am having problems understanding how to calculate the sagitta of R1 and R2. In the Edmund Optics sagitta calculator should I enter the radius as negative, since they are convex?

At the moment I am getting a smaller number for the sagitta of the lens with the longer radius, which does not seem to make sense.



#2 DAVIDG

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Posted 24 May 2024 - 07:42 AM

It does not  make any difference in the calculation if you enter a negative or positive radius  since the sagitta is the difference in height between the edge and the center.  So for a convex surface the sagitta is the value of the how low the the edge is compared to the center.

  The longer the radius the more shallow the curve so the sagitta will be a smaller  value as well. 

     If your going to make a lens I recommend you make a spherometer and also an edge thickness gauge. You also might consider getting the book "Making a Refractor Telescope" since it goes in depth on how to make lenses.

https://shopatsky.co...ctor-telescope 

 

 

                     - Dave 


Edited by DAVIDG, 24 May 2024 - 07:47 AM.

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#3 David Dakstar

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Posted 24 May 2024 - 08:11 AM

I have the book making Making a Refractor Telescope.

The sagitta I get seems very small, for R1 0.0865 inches. I am converting from mm to inches as the Edmund Optics calculator uses mm, maybe I made a mistake?

On the other hand, this is quite a small lens so I guess the sagita will be small. I am used to telescope mirrors.



#4 dan_h

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Posted 24 May 2024 - 09:01 AM

 

At the moment I am getting a smaller number for the sagitta of the lens with the longer radius, which does not seem to make sense.

 The longer focal length lens will have a flatter curve and therefore a smaller sag.  Shorter focal lengths mean stronger curves and deeper sags.

 

dan



#5 DAVIDG

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Posted 24 May 2024 - 09:33 AM

  Sagitta = D2/ (8 R)   so R1 = 16 / (8 x 27.133) =  0.0737"     and for  R2  0.00661" 

 

 

                        - Dave 


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#6 MeridianStarGazer

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Posted 24 May 2024 - 09:44 AM

I would like to make a Schupman telescope. The objective is a double convex lens. 4 inches in diameter. R1 radius is 27.133 inches, R2 radius is 302.400 inches. I have never made a lens and am having problems understanding how to calculate the sagitta of R1 and R2. In the Edmund Optics sagitta calculator should I enter the radius as negative, since they are convex?
At the moment I am getting a smaller number for the sagitta of the lens with the longer radius, which does not seem to make sense.


Divide the radius by 2 to get the focal length of a mirror with that curvature.
Divide that by the diameter to get the f#.
Divide the diameter by 16, and divide this quotient by the f# above. That is the sagitta.

But for a lens, the index of refraction matters.

#7 DAVIDG

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Posted 24 May 2024 - 10:33 AM

 You can simplify the Sagitta formula since the diameter = 2 x radius   so  ( 2 r)2/ (8R)  = 4r2/ (8R)  and that simplifies to r2/2R

 

   so again for a 4" lens with the radius on one side of  27.133"   you get 22/2 x 27.133 = 0.0737"

 

 Making sure the lens blank has enough thickness to grind both sides to the needed  radii. Grind the first surface to the needed sagitta, check your thickness. Grind the second surface, checking the wedge and the thickness as  you go.

 

                 - Dave 


Edited by DAVIDG, 24 May 2024 - 03:07 PM.

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#8 MKV

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Posted 24 May 2024 - 11:36 AM

But for a lens, the index of refraction matters.

No. If you have a lens prescription with known radii of curvature then what Dave is giving you is basically correct. 

 

If you know the lens diameter (D) and the radius of curvature ( R ) of its surface, then the sagitta (s)

 

s = R - SQRT[(R²) - (D/2)²]

 

sqrt = square root

 

Let's say your = 10 mm, and your D = 4 mm. Then

 

s = 10 - SQRT[(10²) - (2)²)] = 10 - SQRT[(96)] = 10 - 9.79796 = 0.20204*

 

Dave's equation will give you 0.2. Is this difference significant?  It can be. It depends on what you're working on. In most case it isn't.

______

 

*This method is accurate if the surface figure is spherical. For aspheric (conic) surfaces, the vertex radius will result in a slightly different value for s.


Edited by MKV, 24 May 2024 - 11:38 AM.


#9 Scott E

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Posted 24 May 2024 - 11:38 PM

If your blank isn't exactly 4" then be sure to se the exact diameter (or radius).



#10 PrestonE

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Posted 25 May 2024 - 07:38 AM

We are working on our 90mm or 3.5 inch BK7 Corrector lenses currently, and find

that a Small Spherometer is really a Necessity!!!

 

A change in 0.0001 inch really moves the Radius when your talking about 218mm/8.58 inch Radius so we

are working with 2 different Spherometers.

 

One has a Contact diameter of about 3 inches and the smaller about 1.4 inches...the smaller

is used to check the consistency of the Radius and measures to 0.00005"

 

Best Regards,

 

Preston


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