Well, I should say that it is kind of dangerous. First, if it is too much, it can hurt your eyeball. And also, because it is made of chemical objects, it can do harm to your eyes. For example, it can make your eyes to be infected. In some serious situation, it can lead to some eye diseases such as pink eyes, dry eyes, and sore eyes. In other words, you should not ignore this problem. In my opinion, you should wash your eyes as soon as possible, and then drop some eye drops so that they can relieve the symptoms. Or you should go and see a eye doctor.
In fact, although cosmetics can make us more beautiful, all cosmetics are harmful to the skin, including mascara. Your eyes will be uncomfortable and turn red if mascara gets in them. You should wash your eyes with lots of warm water at once. Then use several droplets of anti-inflammatory eye drops. A more serious result is eye inflammation and in that situation, you should you go to hospital for treatment. Bad-quality mascara is more harmful to your eyes so you would better choose a good-quality mascara and remove it with eye makeup remover before sleeping.
When the mascara gets into your eyes, your eyes must feel itching because of the irritating stimulations. You'd better get it out by washing the eyes or cleaning the eyes with water and facial tissue. Then have a good rest for the eyes. If you do not deal with it immediately, your eyes will get red which may get the inflammation. You'd better go to see the doctor and use the eye drops.