What characteristic does the pupil exhibit in a patient with cataracts?

In cataracts, the lens of the eye becomes cloudy due to the accumulation of proteins which can lead to a variety of visual disturbances. When examining the pupil of a patient with cataracts, the characteristic it exhibits is a cloudy or milky-white appearance. This is a direct result of the lens opacity caused by the cataract itself, which obstructs the normally clear view that a healthy lens provides.

The other options describe conditions that do not align with the characteristics of cataracts. A clear and bright pupil would indicate a healthy lens with no opacities. A dark and opaque appearance is more characteristic of conditions like amblyopia or certain severe types of eye disease but not cataracts. Shimmering with reflections suggests a degree of clarity and health in the lens, which is contrary to what occurs in cataracts. Therefore, the cloudy and milky-white appearance is the distinguishing characteristic of the pupil in patients suffering from this condition.