I have had a discussion at my university about the following question. Imagine a 'perfect' convex lens and a set of parallel rays, falling onto that lens. The set of incoming rays has a flat intensity profile, i.e. it is equal for all positions along the axis perpendicular to the lens.
Now, after having travelled through the lens, there are two intuitive options for the intensity profile of this set of rays at a distance far away from the lens but before the focal point:
1) it is still flat, since the distance between every ray, although decreased, is still a constant.
2) it decreases with the cosine of the angle of incidence of the ray, just as the intensity of the sun on earth decreases with the cosine of it's angular position in the sky.
Which of the two is right and why is the other not? I tend to say the first one, but I'm not 100% sure.
Also, how does it relate to an actual lens and what is the main reason that an actual lens would never have a flat profile if this would theoretically be the case?