btw, what (k) is best for human eyes? sunlight is 5.5-6k, so I thought white light gives better visablity then lower 4.3k???
The surface temperature of the sun is about 6000 Kelvin, but what we actually see on earth is highly variable, depending on time of day and latitude. Much of the light from the sun is scattered by Rayleigh scattering, so the result is a blue sky, and a (relatively) yellow looking sun. This is why our sensitivity to blue light occurs more in the peripheral vision, and red/green sensitive cones are dominant in the fovea, or central vision used to discern details. The lumen scale is based strictly on central vision. On an overcast day, color temp can be higher, around 7000k. In direct sunlight, during most of the day, color temp will be closer to 4000k.
Another reason this logic (pick the color tmep closest to the sun) isn't always the best is that our eyes work differently depending on the amount of incident light -- generally preferring lower color temperatures as illuminance gets lower. At noon on a sunny day, color temp will be about 6000k, but illuminance will also be as high as 100,000 lux everywhere. One of the common complaints about 6000k+ color temperature bulbs for indoor lighting is that they make things look dreary or dull at the few hundred lux of most homes, they require more lux compared to really look "right". I personally like 5000k at around 1000 lux for task lighting indoors, this is much brighter than most homes and workshops.
Also, the reason why blue light does a poorer job at penetrating fog is actually not due to rayleigh scattering (which is scattering due to particles smaller than the wavelength of light), but due to the fact that our eyes shift toward being more sensitive to blue light at night, and that most objects outdoors preferentially reflect red and green, few things in nature reflect blue. However, fog reflects everything indiscriminantly, so contrast ratio between the illuminated fog and your illuminated object will be much worse.