I read following in a web site (http://realphototips.wordpress.com/tag/ai-servo/)
Lenses with maximum apertures of f2.8 allow the camera to use all high precision sensors. In low light or other situations that are hostile to autofocus, that’s a big deal. Lenses with a maximum aperture of f4.0 use only the center focus sensor in its “high precision” mode, and use the other sensors in their “horizontal line” only mode. Lenses with a maximum aperture of f5.6 use all sensors in their “horizontal-only” mode, and lenses with a maximum aperture of f8 use only the center sensor point, and that with horizontal sensitivity only.
I want to understand if this is completely true? I am raising this because recently I have purchased a Nikon 70-200 f/4 lens and would like to understand if I have made a wise investment, or, should I collect some more money and buy a 70-200 f/2.8 VR-II lens.
When the camera is focussing the lens, the lens is wide open, the aperture is only closed down to the selected setting when you actually close the shutter. So, based on that, an F/2.8 lens will let in twice as much light for autofocusing as the F/4 when wide open.
Did you make a mistake? Possibly not. The Nikon F/4 variants of the F/2.8 lenses are very good and, on modern Nikon bodies, don't suffer from autofocus performance issues at F/4. If you have an older Nikon body, maybe, but if you upgrade your camera at some point, the issue goes away anyways and you still have a nice lens.
Net effect, don't worry too much and enjoy the lens. You might also want to mention what Nikon body you have. :)
There are two factors determined by physics that favor autofocusing with wider apertures.
To take advantage of the wider aperture, the pairs of sensors for a particular focus point in the AF array must be further apart from one another. But that makes those lines not very useful when a lens with a narrower aperture is attached to the lens. So camera manufacturers hedge their bet a little. Some of the focus points are more sensitive/accurate but only function well with a large aperture lens. Other focus points are tuned to be able to use the light from lenses with narrower apertures. But those points can't take advantage of the wider light rays provided by a wide aperture lens.
This is because the two lines on the focus array for each focus point are in a fixed position. If they are close enough to each other to be able to use light that gets through each side of the lens with a narrow f/8 aperture, they are not far enough apart from each other to sense the light that gets through the edge of the lens with a wide f/2.8 or wider aperture. Even when a faster lens is on the camera they are only using light falling on each side of the lens that is close enough to the center to make it through the narrower aperture.
How well the 70-200 f/4 takes advantage of your camera's focus system depends on the specific design parameters of you camera's focus system. In general though, a constant aperture f/4 telephoto lens will perform well. The only place you might be concerned is if you plan to use a tele-converter, since a 1.4X will raise the lens' maximum f-number to 5.6 and a 2X tele-converter will raise it to f/8.
Incidentally, the same physics that favors AF with lenses with wider apertures also favors DSLR cameras with larger sensors. Because the mirror is larger (particularly because it is wider) in a full frame camera than in an APS-C camera, the baseline used for the most sensitive focus points can also be wider.
For a little deeper answer on how cross type points work and a visualization of how f/2.8 points require lines that are further apart, see this answer.
The aperture that controls how much light is received by the AF sensor is the aperture of the PDAF separator lenses which have been shown to be ~f/7. Having the main lens aperture larger does not increase the amount of light. The only time the main lens aperture is relevant is if it is smaller than the AF system is designed for (typically ~ f/5.6).
It's like looking through a paper towel tube (simulating the FOV/aperture of a separator lens)... no matter what size window (main lens aperture) you look through no more light comes through; unless the window is small enough to restrict the FOV farther.
This is probably the best discussion of the topic I have seen (with images).