2
$\begingroup$

I need to find a substance whose refractive index is constantly changing and directly proportional to the square root of the depth. I know I'm looking for a lot, but I'd really appreciate any ideas or advice from anyone. Thanks a lot

$\endgroup$
2
  • 2
    $\begingroup$ Square root or whatever, there is no such compound. In effect, you are asking for a metamaterial with peculiar properties; whether or not it can be made is a separate question. $\endgroup$ May 27, 2017 at 16:48
  • $\begingroup$ There are commercially available optical fibres with a gradient in refractive index, presumably lenses also, often called GRIN lenses. $\endgroup$
    – porphyrin
    Jul 1, 2018 at 7:50

1 Answer 1

2
$\begingroup$

It's not entirely true that no such substance exists, though you won't find this property in a homogeneous substance.

It's well known that changing the concentration of solute in a solution can change the index of refraction; a concentration gradient would then provide a changing refractive index, though having this mimic a square root function would be difficult. Typically, the refractive index changes linearly with the concentration of solute, so a nonlinear function may be difficult to achieve. A similar approach could be applied to solids, forming a solid solution, though again there would be some difficulty in finding two compounds with similar lattice parameters that would allow to a continuous gradient between compositions to product the refractive index gradient.

Your best bet may be with polymers, where changing proportions of the monomers used could change the refractive index; organic dopants can also be used to effect* this gradient in polymers (see, e.g., Polym. Adv. Technol. 2014, 25, 1099). Again, the difficult part would be matching a square-root function, but you could at least have a varying gradient.

*https://xkcd.com/326/

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.