How the conjunctivitis virus spread just by seeing a person's eye who is infected
You can't catch conjunctivitis by looking at someone, but you can spread it around by touching your eye and touching something else, which then can pass the virus to someone else (viral conjunctivitis can be highly contagious). There are no hard facts, but one estimate is that people touch their faces an average of 3.6 times per hour, more if your eyes are itchy. Wearing sunglasses can not only help the possibly increased sensitivity of eyes with conjunctivitis, but they may also cut down on the number of times you touch your eye (thus spreading the virus).

There is no evidence to support that our eye get watery when we see the eyes of an infected person. 

Conjunctivitis (Pink Eye) - CDC
Stop Touching Yourself, Flu Researchers Say