Is there a reason why human eyesight and plants make use of the same wavelength of light?
Good question. 

If you look at the spectral energy distribution in the accepted answer here, we see that photons with wavelengths less than ~300 nm are absorbed by species such as ozone. Much beyond 750 infrared radiation is largely absorbed by species such as water and carbon dioxide. Therefore the vast majority of solar photons reaching the surface have wavelengths that lie between these two extremes.

Therefore, I would suggest that surface organisms will have adapted to use these wavelengths of light whether it be used in photoreceptors or in photosynthesis since these are the wavelengths available; i.e., organisms have adapted to use these wavelengths of light, rather than these wavelengths being special per se (although in the specific case of photosynthesis there is a photon energy sweet spot).

For example this study suggests that some fungi might actually be able to utilize ionizing radiation in metabolism. This suggests that hypothetical organisms on a world bathed in ionizing radiation may evolve mechanisms to utilize this energy.