Quote:
Would you help explain the difference and how our eyes would expect to see this cent "if" we were just using natural bright light and a good loop?
TL;DR at the bottom.
You will see something much closer to the second set of images. The light I used for them is the same one I inspect coins under, in-hand.
I can't say that I'm versed in the scientific theory behind the difference, but here's my thinking:
"Color temperature" is the range of light colors we can see, based on the heat of stars (which is why they call it "temperature") and expressed in Degrees Kelvin, just like star colors. "Cooler" stars are reddish, "hotter" stars range through white into bluish visible color. We can see from about 800 Kelvin (the light cast by a glowing ember, for instance) through about 12,000 Kelvin (the hottest of "blue" stars, and sunlight under certain filtered conditions like in the shade or through a skylight). You and I are used to what is called "warm" colors (a poor name since the word is the opposite of the Kelvin temperature hinted at) offered by typical incandescent lighting and older fluorescent lighting. These are in the 2800-3200 Kelvin range. More modern fluorescents and "Daylight" light bulbs use what's called "cooler" colors (again, the opposite meaning to Kelvin) in the 4500-5500 Kelvin range.
It's why a piece of paper you're reading under incandescent light has a "yellowish" cast to it, while the same sheet of paper read out under the Noon sun looks more "correctly" white. Our eyes see color most "correctly" at color temperatures of around 500-5500 Kelvin. Below that, stuff looks "yellowish" and above that, it looks "bluish."
The Jansjo LED's are narrow-spectrum. They output only a very narrow band of color temperature in the range of temperatures we can actually see. Incandescents are not so limited; they output light across most of the Kelvin range at once although it's heavily concentrated in one specific area of that range.
My first pics are lit with narrow-spectrum LED's. The surfaces of the coin are not nearly as flat as they look, at a more microscopic level, and differing spots reflect that narrow spectrum at different colors die to minute differences in angle and composition. The result is a "speckled" look which doesn't seem "right" compared to what we're used to seeing.
The GE Reveal bulb used for the second images is advertised as a "full-spectrum" bulb, even though it's still stronger in one narrow band of color temperature. It's much less "narrow" than a typical incandescent, but short of the right to be called a true "full-spectrum" bulb like a plant grow light.
Under this light, the individual spots on the coin each receive a broad spectrum of light color, and therefore reflect more closely to all of their fellows. This results in a much more "homogeneous" look to surface color, something we perceive as more "appropriate" since it's how we've learned to see coins under the light we're used to.
Wow, that turned out longer than I'd hoped, and as a result probably didn't help much.

TL;DR takeaways:
1) Narrow-spectrum bulbs lead to a "speckled" look, because surfaces aren't even on a more microscopic level and they only have one color of light to reflect.
2) Broad spectrum bulbs lend a look more like we're used to, because that's what we usually look at coins with, and they're reflecting all colors of light at once.
3) If you look at your coins in-hand under a narrow-spectrum bulb, you'll see the same thing the camera does.
4) Looking at the same coin, you probably won't see what I do, because you're using a different light. Same goes for your camera, because you're probably using different lighting for it, too.
5) The difference between narrow-spectrum and full-spectrum lighting
matters until you learn to make conscious allowances for how the light is "deceiving" you.