Yes, eyes are connected with brain, functionally and physically. There are two kinds of cells in eyes, named as rodes and cones after their shape. Rode are good at picking up faint light signals, while cones can pick up a wide rang of colors and they are very good at reading details. Light travels into eyes and get focused on the retina. It transmit the light to the brain as electrical impulses through optical nerves. Optical nerves are also known as cranial nerve 2, which is responsible for transmitting visual signals to the brain. It is considered to be part of the central nerve system, connecting eyes and brain. As to impact that brain could bring to eyes, there are too much to say. We know that brain is the central command of human body. It controls every movement we make, as simple as blink, turning eyeball, walking, talking, thinking and understanding. Once the brain is diseased, it surely will impact our body. This is why a stroke could cause vision impairment.
