You can estimate the resolving power of your eye with a sample experiment. Make black stripes of equal width separated by white stripes: see figure here.
All the black strip should be of equal width, while the width of the intermediate white strip should increase as you go from left to right. For example, let all black stripes have a width of 5 mm. Let the width of the first two white stripes be 0.5 mm each, the next two white stripes be 1 mm each, the next two 1.5 mm each, etc. Paste this pattern on a wall in a room or laboratory, at the height of your eye.
Now watch the pattern preferably with one eye. By moving away or closer to the wall, find the position where you can just see some two black stripes as separate stripes. All the black stripes to the left of this stripe should merge into one another and would not be distinguishable. On the other hand, the black stripes to the right of this would be more and more clearly visible. Note the width 'd' of the white stripe which separates the two regions, and measure the distance 'D' of the wall from your eye.
Then d/D is the resolution of your eye.
You have watched specks of dust floating in air in a sunbeam entering through your window. Find the distance (of a speck) which you can clearly see and distinguish from a neighbouring speck. Knowing the resolution of your eye and the distance of the speck, estimate the size of the speck of dust.