How things appear to naked eyes at very high frequencies? We know after a certain frequency our eyes cannot see the changes but how to predict what should be the steady state appearance (of things changing at much higher frequencies )seen by the eyes ?
For more context
example - if we apply a square wave (at a very high Frequency) voltage across a LED , why we see continuous glow instead of no glow at all at steady state (although both condition are possible )? So how we predict that eyes see " always glow state" and not the no glow State ?
Similarly - if a bulb changes its colour in order VIBGYOR and repeats at a very high Frequency then again what will our eyes see (which color ) at steady state and how to predict this ?
 A: The perceived state of a rapidly and periodically changing object will be the time average of its actual state. The rapidly flashing LED is perceived as continuously on, but with a reduced intensity which depends on its duty cycle - this is the principle behind pulse-width modulation of LEDS. The colour cycling LED will appear white or near white, assuming the intensities and periods of its separate colours are equal.
A: The photoreceptors of the eye (and the neurons collecting and transmitting the signals) have particular timescales for their responses. So when a very rapid square wave arrives the receptors do not have time to return to the dark state. That is why it looks bright rather than dark. Similarly flashing different colours will stimulate different photoreceptors in turn, but do it fast enough and they will all keep on responding continuously and you will see a mixed colour.
While the rhodopsin pigment changes conformation within 100 femtoseconds of being hit by a photon, it then causes conformation changes in the protein it is embedded in over nanosecond timescales, which in turn activates a G-protein that in turn activates second messenger systems that makes the membrane potential change over millisecond timescales. Rod cells have timescales of 200 milliseconds (above 25 Hz flickering things look steady in dark vision), while cones are faster (above 60Hz colors and bright light vision looks steady).
So when you flicker faster than the flicker fusion threshold, things look steady. This is just one of many persistence of vision phenomena.
