I'm using a stinking tripod
Sorry, I thought you'd mentioned in a past post that you hadn't gotten one yet. My mistake.
I didn't try the pop-up flash because it was just one more variable to work with. Even with the tripod, this was a bit of a task. Maybe I can get my girlfriend to assist me in my next attempt. Are you recommending thy I focus the onboard flash by having someone hold a mirror up to reflect it onto the water drop? Willing to try that.
No mirror should be necessary to simply hit the droplet with the built-in flash. Last time I checked, it was pointed the same direction as the lens. You may get a small shadow on the bottom of the image, but you're going to be cropping the image anyway, so this is probably a non-issue here. The mirror I'm suggesting would be held at a 45-degree angle to reflect the light onto a nearby wall or ceiling, so that the light bounces and comes at the droplet from the side or above, and from a nice large surface area.
The off-lens-axis direction determines the location of shadows, which give a 'shaping' or 'modeling' effect (seen in your examples). Straight-on flash lacks this effect, because everything is is lit from the front, giving almost no visible shadows.
The large surface area helps with softness of said shadows. When the light source is a point-point (like the direct unmodified flash itself), you get crisp-edged shadows, which are almost always ugly.
If no white wall or ceiling is handy, shooting through a white piece of paper or napkin will give you the larger light source, but without the help of side- or top-lighting.
And for eliminating variables - here's a cheat sheet to get you started:
Manual mode: 1/200 sec, f/11, ISO 400. Pop up the flash, and use its +/- Flash Exposure Compensation to get a brighter or darker shot. Tweak f-stop and ISO if you're getting grossly underexposed shots.
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