We all know when fan starts moving faster, we cannot see its blades. Why is this?
First I assumed persistence of vision may be the reason. But that can happen with blade also right? Image of blade can remain in our memory and moving fan can appears as a circular plane with blade color.
Why only image of rear side of fan is remaining in our memory?
Note: I tried with fan whose blade area is almost same as that of non blade area
The eyes are measuring the number of photons of each color that are hitting a given point of the retina – that are coming from some direction.
This is a function of time, $f(t)$, for each point. However, when this function is changing too quickly, the eye can't see the changes. Effectively, the eye may also see the average of $f(t)$ in each period of time which is as short as 1/50 second or so. That's why 24 or 25 or 30 or 50 frames per second are usually enough for a TV screen.
If the fan frequency is at least 1 blade per 1/50 second, which is the same as 10 rotations per second for a 5-blade fan, for example, the following is true:
During 1/50 seconds, each point of the image where fan blade may either be or not be sees a full period, so the perception is no different from the perception in which the color is averaged over those 1/50 seconds. But the averaged color of each point is pretty much the same. It's a weighted average of the (RGB) color of the objects behind the fan at the given point; and the color of the fan blade. The weights in the weighted average are determined by the thickness of the fan blades (relatively to the circumference), and these weights may actually depend on the radial coordinate $r$.
So what we see is not "quite" transparent – the contrast is lower – but it's enough to see what's behind; the color of the things behind the fan is mixed with the color of the blades; and this mixing occurs pretty much independently of the location relatively to the axis of the fan (if the fan blades' color is uniform), and independently of time (because of the averaging over the 1/50 second time intervals).
Note that the 1/50 second resolution depends on the neurology – abilities of the eye, nerves, brain etc. However, even if the brain were perfect, there would exist certain limitations that couldn't be beaten. The number of photons coming to each retina cells per second is finite and the inverse of this number basically determines the best possible time resolution one can have for the given "pixel".
Because human eyes and brains are slow, they cannot resolve the motion of the blades, but only see the average of the moving blades and the image in the background (this is actually primarily really due to the slow reaction time of the cones, which is slow, as is demonstrated by the fact that a 24 frames per second video does not appear as single images but in motion). Due to their motion the blades average more or less to a uniform colour, so only the image in the background is seen.
If your eyes follow the motion of the blades for a short time (eyes can track pretty fast objects), it is nevertheless possible to resolve the shape of the blades for a short time.
But summarized: The image of the blades is not even resolved by the retina, so it will certainly not be processed by your brain and leave a memory.
As to the perception of the image in the background vs. the moving blades as uniform disk of colour, those are the attention mechanisms of the human image processing. It is for the same reason that you can decide to watch the bottom of a pond or the reflection on the water surface.
The answer is that your view or sight is different from the bare images made by the imaging optics of your eye on your retina. A "view" also includes signal processing from the brain that tracks what you fix your gaze on.
Light can pass between the blades and form an image of the retina for at least some time. It's true that there are also blades blocking your view some of the time. But the brain detects meaningful information in the light coming from beyond the blades, and accordingly your eyes will focus on points beyond the blades. The blades therefore do not form sharp images on the retina and instead light from them simply shows up as low level, approximately uniform illumination on the retina whose level is much below that from in-focus objects. The brain will thus throw this information away as noise.
It's an interesting experiment to try (which I have just done) to look through a fan and try to focus on the blades. When you do so, you cannot see them (probably because the brain's signal processing is not fast enough to track them) and, at the same time, images of things beyond the fan blur and drop out of view.
One way to think of this is to imagine a high-speed camera which takes 1000 frames per second (which is 40x as many as a regular film camera). Then imagine putting the frames into groups of 40, and averaging each group, so that you now have a film with a normal framerate, where each frame is the average of 40 high speed frames. The resulting film would be similar to what your brain perceives when you watch the fan.
