what is the term for broken capillaries in the eyes?
Vigorous coughing is one possible reason for burst eye capillaries. Photo Credit Thinkstock/Stockbyte/Getty Images. When a capillary in the white part of the eye bursts -- called a subconjunctival hemorrhage -- the appearance of blood can be rather dramatic and alarming. Often, there is no history of trauma to the eye -- the blood simply appears spontaneously.