My theory is limited in this regard so I had a little doubt. I often see it mentioned in the problems that "assume aperture size of lens much smaller than its focal length" what does this signify? What would happens if they were comparable?
It is often told to take the aperture of mirrors very small , as elementary physics deals with paraxial rays (i.e rays which passes very close to principal axis). Well if aperture is large then rays can fall far away from the principal axis which will not remain a paraxial ray any more and it will be complex to deal with such rays. For example only paraxial rays pass through focus when ray is parallel to principal axis where as non-paraxial rays misses the focus resulting complex calculations.