Vision jumpy only for specific frequencies?

I wasn’t quite sure how to title this question, but it’s an odd phenomenon that I’ve noticed - when using my electric toothbrush, the light on my humidifier will appear to jump around, moving rapidly up and down (it looks like it is moving maybe ~1/2 cm or 1/4 inch) - yet everything else in my vision seems perfectly stable. Can anyone explain why this happens? I am not quite sure what kind of light the humidifier has, but I assume it is some kind of LED. I believe my clock also uses LEDs and it doesn’t move around at all when using this particular toothbrush - but when I tried using my wife’s electric toothbrush some time ago, which vibrates at a much higher frequency, I seem to recall the clock display jumping around in a similar manner.

I assume my eye or other parts of my head actually are vibrating along with the toothbrush, so why does my vision seem so stable outside of this one particular light? Do our brains use some kind of image stabilization, or does this have something to do with persistence of vision?

LEDs aren’t actually constantly lit. They actually flicker on and off at a higher frequency that people can ordinarily discern, so they appear to be constantly lit to our primitive eyes (relying on persistence of vision, which you noted). The vibrating toothbrush causes your head to vibrate at some frequency. If there is some resonance between the frequency of the light flashing and your head vibrating, you may get weird effects, like seeing two seemingly stable points of LED light at the points where your head happens to fall in its vibration cycle when the LED is lit. I am guessing that your toothbrush resonates with the LED on the humidifier while your wife’s electric toothbrush resonates with your LED clock.

With many illuminated indicators, Christmas lights, or small appliance lights, I have noted that quickly flicking my eyes side to side while looking at the light is an easy way see if it is an LED. Instead of seeing a continuous blurred or smeared streak of light, LEDs leave a trail of distinct repeated images across my field of vision. This often works better if the general illumination level in the room is low.

I have always assumed the LED flicker occurs at 60 hertz, the frequency of AC power in the USA. (50 hertz for the rest of the planet.)

No. LEDs do not inherently flicker. You can drive an LED with a steady supply (constant current supply, or constant voltage with appropriate resistor - such as a battery) and there will be no flicker at all.

That said, many LEDs are driven by power supplies that aren’t steady and lead to flicker:

  • AC mains directly with no rectifier. LED is on somewhat less than 50% of the time (depending on specific voltages).
  • AC mains with full-wave rectifier. LED will be on somewhat less than 100% of the time.
  • DC power through a multiplexer so a microcontroller/CPU can drive N LED with fewer than N outputs. Each LED will be lit about 1/N of the time when “on”, where N is generally the number of multiplexer outputs (which may be more than the number of LEDs installed).
  • DC power with a pulse-width modulation driver (PWM) for dimming (either to provide variable brightness, or just as an easy way to bring a given LED down from “insanely bringer” to “reasonable”). LED will be on some fraction of the time.