Final answer:
The ciliary muscle controls the tension of the suspensory ligaments of the lens.
Step-by-step explanation:
The structure that controls the tension of the suspensory ligaments of the lens is the ciliary muscle. The ciliary body, which is a muscular structure attached to the lens by suspensory ligaments, is responsible for adjusting the shape of the lens to focus light on the back of the eye. When the ciliary muscle contracts, the suspensory ligaments relax, allowing the lens to become more convex for near vision. When the ciliary muscle relaxes, the suspensory ligaments tighten, making the lens less convex for distance vision.