Ok, the title may be a little misleading. More like: Could a person with good sight detect the presence of a black dot (against a light background) the size of an E. coli bacterium?
This cite says: “Each bacterium measures approximately 0.5 μm in width by 2 μm in length.”
I am young(ish) and have pretty good close vision (I am nearsighted). I stuck a ruler directly under my eye and the first number that was totally clear was 13 cm. So now I need to know how small of an arc something can be and be seen.
According to Wikipedia: “The smallest detectable visual angle produced by a single fine dark line against a uniformly illuminated background is also much less than foveal cone size or regular visual acuity. In this case, under optimal conditions, the limit is about 0.5 arc seconds or only about 2% of the diameter of a foveal cone. This produces a contrast of about 1% with the illumination of surrounding cones. The mechanism of detection is the ability to detect such small differences in contrast or illumination, and does not depend on the angular width of the bar, which cannot be discerned. Thus as the line gets finer, it appears to get fainter but not thinner."
A bacterium is not a line, so let’s be conservative and double the value from 0.5 arc seconds to 1 arc second.
According to this website: 1 arc second at 130mm is 6.3e-4mm. So that is 0.63 μm, which is less than the length of an e.coli.
So, reviewing my original question: Can a person detect the presence of a black dot (against a light background) the size of an E. coli bacterium?
Okay, I just made this image. Somewhere on it is a single black pixel. (Hopefully your monitor is native 1920x1080.) See if you can see that under your preferred viewing conditions. Then you can compare the size of that pixel (going from the dimensions of your monitor) to the size of an E. coli.
However, that visual acuity is the ability to see two object as distinct (not as a whole). That is not the same thing as being able to detect the presence of something.
Which is why I said “Then you can compare the size of that pixel (going from the dimensions of your monitor) to the size of an E. coli.” Meaning “if I know this pixel looks this size, and I know that a bacterium would look that size, then that’s how much smaller it would be.”
Ok, I can go with that suggestion. Maybe a little bit of practical science is needed to help out here. I don’t have optimal conditions (or the youngest eyes), but I put a black ink dot on yellow sticky note. Under close inspection with a mm ruler, I judged it to be approximately 1/2 of a mm wide.
I stuck it on the wall and then I kept going closer and farther until I was juuuust on the cusp of being able to detect it. That distance was 10 feet (give or take a few inches). Using the handy dandy calculator mentioned previously, that gives me a detection size of 34 arcseconds.
Maybe under laboratory optimal conditions and with someone with really good eyes, they might be able to get down to 20 arcseconds. That still means they could only detect something down to 12 microns.
That is too large to detect a dot the size of an E. coli. However, it is the size of plenty of humans cells!