Final answer:
A non-reflective coating that is effective at all wavelengths would ideally have a low index of refraction and be thin, similar to that of a soap bubble.
Making this practical, however, is challenging due to the requirement of having a consistent thickness across different wavelengths for perfect destructive interference.
Step-by-step explanation:
To create a non-reflective coating for lenses that is effective at all wavelengths, the inventors must pay attention to the index of refraction and the thickness of the coating.
For destructive interference to occur at all visible wavelengths, the coating should have an optical path length that is a half-integer multiple of the wavelength of the incident light. Revisiting the observation of a soap bubble being dark at its thinnest point, we recognize this is due to destructive interference when the thickness of the bubble is just a quarter of the wavelength of the light.
To minimize reflection across all wavelengths, the coating thickness would ideally be such that the optical path difference (the extra distance traveled by a wave that reflects off the bottom surface of the film plus any phase changes upon reflection) is half a wavelength.
Considering the practical aspect, the best choice among the provided options would likely be to use a low index of refraction and a small thickness, similar to that of the thin film on a soap bubble. This method could be practical for eyeglass lenses which are option (c).
However, making such a coating that is effective at all wavelengths can be impractical because each wavelength would require a slightly different thickness for perfect destructive interference.
This could lead to challenges in manufacturing such coatings that are both thin enough and also consistent in thickness across the entire surface of the lens.