Found original part?

[Dyne]

The glass lens is pretty massive, and i have no idea ho to measure the curve.

After several months of illness- and politics-induced loss of motivation, a 3d printer that I thought was broken, and just time getting away from me, I'm finally back to working on (aka "starting") my Treadwell build.  Printed out savage's STL, and I was reminded about the lens question.

It's pretty obvious that the outer face of this lens (as used on Treadwell) is convex, but I can't tell from the photos whether the inner face is flat, convex, or concave.   Whatever the case, it's not difficult to measure the curvature of a simple spherical lens, which is what this probably is.  As implied by the name, a spherical lens is just a slice of a sphere.

The simplest case is a plano-convex lens (the back face of the lens is flat).  We've all seen edge-on cross sections of this type of lens.  It's basically a rectangle with one edge curved outward (I put a line between the rectangular section and the curved section):


The part that we care most about for modeling purposes is the lighter blue section.  As you might guess, that bit is just a slice out of a circle.  It's bordered by an arc (curved line on top) and a chord (the horizontal line between the two sections).  The radius of the arc is equal to the radius of the circle it comes from, which in turn is equal to the radius of the sphere that the lens comes from.

To get the radius of the arc, you need two measurements:

• W is the green horizontal line.  It's the length of the chord ... or in other words, the diameter of the lens.  Since this particular lens is likely not a full disc shape, but instead squared off to fit into its holder, I'd suggest measuring at its widest diameter (i.e. across the square from "corner" to "corner").
  
• H is the small purple vertical line.  It's the height of the arc, aka the distance that the lens protrudes out from the point where you measured the diameter.  Alternately, if you know the maximum thickness of the lens, you can subtract the height of the darker rectangle (which we'd eventually want to know anyway).
  

Once you have H and W, you just use this formula:

( (W^2) / (8H) ) + (H/2)

For a lens with diameter of 60 mm and an H of 5 mm, this would work out as ( 3600 / 40 ) + 2.5, or a sphere of radius 92.5 millimeters.  Once you know that, you can take measurements like the thickness of that darker rectangle, then reproduce the lens in CAD :



I measured that sketch in Fusion 360, and the width of the resulting lens shape is indeed exactly 60 mm.


A biconvex lens -- both faces are convex -- isn't much worse.  It's just two of the above, back-to-back.  There's a good chance that this sort of lens is symmetrical, both faces having identical curvature.  But it is possible that they aren't the same.  The curvature of the inner face probably doesn't matter much unless you want to take screen accuracy to an extreme.



A meniscus lens (one face convex, the other concave, like eyeglasses) can be treated like two convex lenses pointing in the same direction, but the one on the concave side subtracts material from the lens rather than adding to it.



If someone can give me the relevant measurements, I can try my hand at modeling the thing.  At the very least one could print a mockup, sand it smooth, and paint it black.