I’m outside on my phone right now and a very light rain started. One raindrop in particular that landed on the screen formed a dome maybe 2 or 3 millimeters across, and magnified in that dome I could very clearly see individual square red/green/blue sub pixels with a very thin grid of black lines around them. With a roughly 300 pixel per inch density, I can’t see the subpixels with my naked eye even with the screen held as close as my eyes can focus.
That got me wondering–about how high of a magnification can you get from a drop of water flattened on a surface? I know that a Leeuwenhoek microscope is essentially a spherical “drop of glass” and can magnify over 200x.
Note that the refractive index of glass is higher than that of water, so you can essentially get “more magnification” (that’s a simplification, there’s more to it than just that).
The basic answer is “it depends on the size of the drop” - smaller drops magnify more because they’re more curved - but I’ve seen figures quoted anywhere from 5-20 (this site says 5-10).
A fun thing to do is use a water drop on your mobile’s lensto take macro photos.
Complex question.
In the first place, your magnifier is a water drop directly on the surface it’s magnifying, so you don’t use the standard lens formula.
The smaller the drop size, the smaller the radius of curvature, and the shorter the focal length and the greater the magnification. But as you make the droplet smaller and smaller you have less of a viewing area, and eventually diffraction is going to start becoming a problem.
Leewenhoek’s microscopes were single-lensed instruments, basically tiny magnifying glasses. Leewenhoek was a superb lens grinder who made nearly perfect nearly spherical lenses that had to be placed very close to the subject. Having a biconvex lens meant that its power was greater than a plano-convex lens. Also, glass has a higher refractive index than water, so a glass sphere has a shorter focal length/higher power than a water drop the same size. (You CAN make a nearly spherical water drop microscope. You need an almost perfect hole punched in a piece of metal or clean cardboard – like a playing card. If you bend the ends of the metal or cardboard strip so it supports the ends, you’re almost there. Use an eyedropper to place a drop of water in the hole and you’re there. You focus by pushing lightly on the strip to move it towards or away from the subject, placed underneath.) How great a magnification can you get? Most sites I’ve checked claim its a relatively low 5-10X, but I haven’t run the numbers myself.