During a biology experiment at school, where we would look at waterweeds under a microscope, my teacher said something about that it's impossible for the human eye to see the cells without a magnifying glass of some sort. So, I saw that as a challenge, and decided to check if I could see the cells. And after holding the leaves really close to my face, I was indeed able to see tiny rectangles.
Since I was curious about it now, I decided to look some more things up. First, I tried to find out the actual size of waterweed cells. Based on this 640x enlarged image, which features cells of 5mm wide and 10 - 15mm long in the picture (which corresponds with of roughly 8µm wide and 15µm long).
I left this in the back of my head for a long time then, but I just looked at my cotton sleeve, and noticed tiny fibers. Not the ones that are woven together, but ones that are standing out from it. So, after looking it up, it turns out that cotton fibers are 10 µm wide.
So, I wondered, what is the smallest size a human eye can actually see? According to a whole bunch of sources all across the internet, it's either 200-400µm, 100µm, or 58-75µm. I also hear 'the width of a human hair' very often, but those can range from 17 to 181µm.