Why does shorter focal length result in greater beam divergence? So I got 2 converging Fresnel lenses, one with 50 mm focal length and other 70 mm. 
My experiment looks like this:

When trying to focus and SMD LED emitter into a narrow beam (sticking to lenses focal length accordingly), the one with shorter focal length gives bigger divergence (measuring spot on the wall).
I assume this has something to do with smaller angle of incidence, but running the simulation with "ideal" lens shows no difference in divergence between two cases with different angle of incidence.
(On the figure 2, distance between A and b is equal)
Also, I am not sure whether they are aspherical (does it apply to fresnels?) and if no maybe this is the issue?

 A: When the LED is placed $50mm$ from the lens, its etendue (the product of its size and the solid angle into which the LED radiates light, subtended by the lens) is greater than the etendue of the same LED placed $70mm$ from the lens of, presumably, the same size.
Therefore, due to the conservation of etendue, the divergence (solid angle) of the beam after the lens will be greater in the first scenario, i.e., for the $50mm$ lens.
A: D. Duck has the best explanation - Here is a picture of what he (or she) is describing (I hope the picture shows up, pictures are helpful). This is for the case of f=50 and f=100, so that the difference in field angle is more apparent. This is what D. Duck is getting at by speaking of divergence - the field angle is set by the ray from the top of the object and goes through the center of the collimating lens. This field angle is higher for the shorter focal length lens. The ray from the top of the object through the center of the stop (in this case the collimating lens) is called the chief ray.  The higher field angle will result in a larger spot after you go any appreciable distance (like across the room).
Although this problem is related to etendue, using etendue to explain this can be unecessarily confusing. In particular, the etendue argument presumes the lenses are the same size, and that may not be the case. It is simpler to show the path of the chief ray.  Here is one useful formula:
   chief_ray_angle = atan( LED_diameter / 2 / focal_length)

