I am reading the wikipedia page for parabolic antennas, and have a question about the below quote:
In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used
Why is this so? The geometric explanation of these antennas doesn't really explain it---from what I understand, the paraboloid has a unique property:
The lengths of $FP_1Q_1 = FP_2Q_2 = FP_3Q_3$.
So if we emit light at the point $F$, and coat a paraboloid in a mirror-like material, it should send the light in a straight beam (following the $FP_1Q_1$, $FP_2Q_2$, $FP_3Q_3$, etc lines) parallel to the line $VF$, no matter the wavelength.
So why do the dishes need to be bigger than their wavelength?