A person struggling to quickly adjust their vision from looking at a distant, dim object to a much closer, bright object is likely experiencing difficulty with accommodation, the eye's ability to change focus between near and far objects. 

During accommodation (the eye's process of focusing), the pupil constricts (gets smaller), and the lens becomes thicker. This thickening of the lens is caused by the ciliary muscles contracting, which relaxes the suspensory ligaments holding the lens in place, allowing it to become more rounded and thus thicker. The pupil constriction helps to increase the depth of focus and reduce light scattering at the periphery of the cornea, further improving the clarity of the image.