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It seems to me, that a bi-convex lens could be replaced by two plano-convex lenses, positioned plano-to-plano with zero separation, to the same effect.

Is that true? What are the downsides? Should they be glued or the gap oiled and taped? I assume there is some reduction of transmitted light.

I ask, because I am trying to assemble a telescope that calls for a lens thicker than any affordable glass, but less than twice as thick as what I have.

An alternative solution is to fuse two thick sheets of plate glass together. This works well for a front surface mirror, but I wonder about a refractive element where the fused boundary has light moving through it. Does anyone know if the fused boundary zone will be a source of significant aberrations?

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    $\begingroup$ You should say some more about your project. A system sketch would help you. In theory what you ask is true - even if you mount them with a 100 micron airgap spaced by a shim it'll be a good approximation. But if you're trying to build a diffraction limited telescope, there are a good many more variables to think about than thickness of lens. You may well be able to buy a precision aspheric for your project for a couple of hundred dollars - again - it all depends on what you are trying to do. What do you want your telescope to do - see stars, spectroscopy, ....? $\endgroup$
    – Selene Routley
    Jan 11, 2017 at 1:05
  • $\begingroup$ It is not clear what you are asking. If the combination is the same material and occupies the same shape, it will have the same focal length. But then you mention a lens less than twice as thick as you have. Finally, the alternative solution of plate glass would not act as a lens at all. Your question is confused. $\endgroup$
    – sammy gerbil
    Jan 11, 2017 at 2:11
  • $\begingroup$ My comment about fusing plate glass to make thicker glass meant to imply I would then grind the fused glass into the shape of the needed lens. My question, was does the fusion result in aberration internally at the plane of fusion within the ground lens? $\endgroup$
    – gbambo
    Jan 19, 2017 at 21:44

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First about the theory, you can of course put two plano-convex lenses back to back and obtain a biconvex. However the resulting biconvex will have half the focal length of the plano-convex. Furthermore, aberrations with a biconvex lens are worse than with a plano-convex in the case of an infinite-focal point conjugation. But this depends on your configuration of course!

Second about how to stick together the two lenses, I think there are usual UV optical glues but they are very difficult to use correctly and the lenses must be perfectly clean of course. If done correctly it should not be very bad regarding transmission.

Now I am not sure to understand what you are trying to achieve. Where are you planning to put a lens in your telescope? And what prevents you from buying a biconvex lens directly if you need one?

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    $\begingroup$ The reason I cannot buy a biconvex lens is that the lens will be used as a full aperture corrector in front of the mirror. Buying a 400mm biconvex lens that is 35mm thick at center is prohibitive. But grinding it is entirely feasible. But obtaining 35mm thick glass is not affordable. I have ready access to 19mm thick glass though. Focal length of single plano-convex lens is different that focal length of the bi-convex lens. But is the focal length of the sub-system of two back-to-back (plano-to-plano) plano-convex lenses different than that of the single bi-convex lens? Why would that be? $\endgroup$
    – gbambo
    Jan 11, 2017 at 0:38
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    $\begingroup$ Ok I am not ultra familiar with homemade telescopes but grinding yourself an aperture corrector sounds like way more complicated than grinding a primary mirror. Also I say that out of memory but I think aperture correctors usually are meniscus so I would not recommend using a biconvex lens. Does this solution rest on any calculations or known geometry you want to use? What about only a plano-convex lens? It is simpler but maybe to thick for your application... finally I would add that using a single lens will bring you a lot of chromatic aberrations. $\endgroup$
    – Raphaël
    Jan 11, 2017 at 0:51
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    $\begingroup$ Your points are well taken. My design is by a world reknowned Russian optician. The corrector is multi-lens. Ordinary aperture correctors are complex in figure, refering to the standard Schmedt corrector plate. My project relies on a recent innovation. $\endgroup$
    – gbambo
    Jan 11, 2017 at 3:56
  • $\begingroup$ But you are mistaken I believe, about a spherical lens being more demanding than a mirror. Mirrors redirect light at angles usually greater than 90 degrees. Lenses bend light very, very mildly in comparison. As such, their tolerances are far below that of a mirror. Further, a mirror doubles it error by operating through reflection, contrary transmissive optics. $\endgroup$
    – gbambo
    Jan 11, 2017 at 4:04
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    $\begingroup$ But lenses have chromatic aberration due to dispersion of the glass - something that mirrors lack. $\endgroup$
    – Floris
    Aug 19, 2017 at 2:16

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