Addendum: 4pm MDT, April 28th:
It's back... the sunspot that launched the biggest measured solar flare on record a few weeks ago, even AR9393, is back around on our side of the sun again. If you want, you can look at it with binoculars.Do not look THROUGH the binoculars at it. Put those down, you idiot. You keep that up and you'll go blind. Fast. We might even hear the sizzling noises while Sol's focused rays boil your eyeball. No, it goes like this: cap one of the binoc lenses, and then point the binoc's big lens at a the sun, and small lens at a white paper plate (or sheet of bristol board, for my webtooning buddies out there who are more likely to have bristol board lying around than paper plates). Focus...
When you see a sun-shaped (that's round with sharp edges) bright image on the plate, you'll also be able to see a speck on it. This speck is roughly 14 times the size of our planet's shadow (assuming, for a moment, that our planet could cast a shadow ON the sun--the thought of being back-lit by something that bright makes me nervous).
For obvious reasons, this experiment works only in direct sunlight, and never works at night. For not-so-obvious reasons, NASA was able to watch sunspot AR9393 when it was on the far side of the sun. Read up.
Addendum: 4pm MDT, April 28th: I performed the experiment several times today. Optimal distance from binocs to paper seems to be between 50 and 100cm (between 19 and 39 inches). I actually saw four specks, and one of them was much larger than any of the others. It looked like the binoc lens might be dirty. So I rotated the binocs, and the specks stayed put. Them's sunspots.
I also tried to see if I could burn myself with the binocular-focused sun. My finger got pretty toasty, but not burnt (yes, yes, I tried to burn paper first--not hot enough). Now, imagine that uncomfortable-but-not-quite-scorching heat on your eyeball, being focused AGAIN by the lens on your eye. I'm not kidding around here, people--if you look at the sun through binoculars, that bright white light will be the last thing you see for the rest of your life.