A lot of long, detailed, technically correct answers already, so I'll try to add a simple explanation.
TL;DR The sizes of the lens elements have some influence on the vield of view, but not the way you describe in your question.
The lens opening diameter does not determine the field of view. Imagine a (horrible-quality) single-element lens with 5mm diameter ...
(editing or comments welcomed)
For an APS-C sensor, the equivalent of a full-frame lens of focal length F and maximum aperture N has a focal length F/1.5 and a maximal aperture N/1.5 (ie the equivalent of a FF 50mm f2.8 would be an APS-C 33mm f1.8).
A comparison, taking into account this equivalence, of existing objectives shows that the ...
Angular Field and Angle of View
Lens makers use the term “angular field”, which is the angle as measured from the center (axis) of the lens. Thus, a lens with an angular field of 20° to the photographer will be an angle of view of 40°.
TV sets are sold by their corner-to-corner (diagonal) measure because this is the largest dimension of the rectangular ...
Then why aperture for APS-C has to be 25mm?
Because the f-number is a measure of focal length divided by the diameter of the entrance pupil. That is, the focal length of the lens divided by how wide the aperture looks when viewed from the subject's position in front of the lens.
But its a fact APS-C lenses are cheaper than FF lenses, so they must have less ...
The lens' angle of view (AoV) is the same regardless of what camera it is on. The system's AoV is the combination of the lens' AoV and the sensor's AoV.
"If we talking about manual focus lens from FF camera i can use it on APS-C camera then i will get different field of view so about 33% of outer side of the lens will not be used?"
That part is ...
The difference in angle of view is due to the smaller image sensor size, not the lens or it's aperture.
APS-C lenses can be made cheaper and smaller because their image circle only has to cover the smaller image sensor on APS-C cameras.