The ghost of Julius Caesar appears to Brutus in Act IV scene 2. When Brutus is left by himself, he sees the apparition appear to him, and he greets it with the following words:
How ill this taper burns! Ha! who comes here?
I think it is the weakness of mine eyes
That shapes this monstrous apparition.
It comes upon me. Art thou any thing?
Art thou some god, some angel, or some devil,
That makest my blood cold and my hair to stare?
Speak to me what thou art.
Clearly, from the quote above we can see that the ghost does make Brutus feel scared and terrified, as is shown through the description of his blood being "cold." However, interestingly, in the conversation that he has with the ghost and how the ghost tells him that they will meet again in Philippi, Brutus seems to speak in quite measured tones and appears to be not so concerned. However, when the ghost does disappear, Brutus finds himself desiring to speak more with it and is frustrated that he is unable to do so. He wakes his servants to try and establish whether they saw any apparition as well, or whether it was just him.