The ancient Greeks were basically divided into two camps of how vision works. One camp held with the theory of Emission (or extramission) in which visual perception comes from light beams which come out of the eyes. This view was held by Socrates, Plato and many others.
The opposing view held that miniature replicas of objects entered into the eye. This is the intromission theory and was an opinion held by Aristotle, Galen and others. These miniature replicas were called eidola and somehow represented the 'spirit' of the object being viewed.
(In fact there are another couple of theories which are kind of sub-categories of these, but I'm not knowledgable enough to explain the distinctions fully. Here are a couple of interesting articles that I found.
It seems to me that there are several examples in the Gemara which appear to side with the first opinion, that sight comes from light emmitted by the eyes.
The verse referring to Elisha states (II Melachim 2:24)
וַיִּפֶן אַחֲרָיו וַיִּרְאֵם, וַיְקַלְלֵם בְּשֵׁם יְהוָה; וַתֵּצֶאנָה שְׁתַּיִם דֻּבִּים, מִן-הַיַּעַר, וַתְּבַקַּעְנָה מֵהֶם, אַרְבָּעִים וּשְׁנֵי יְלָדִים.
And he looked behind him and saw them, and cursed them in the name of the LORD. And there came forth two she-bears out of the wood, and tore forty and two children of them
The Gemara explains this in Sotah (46a), stating:
מה ראה אמר רב ראה ממש כדתניא רבן שמעון בן גמליאל אומר כל מקום שנתנו חכמים עיניהם או מיתה או עוני
And he looked behind him and saw them, and cursed them in the name of the Lord. What did he see? — Rab said: He actually looked upon them, as it has been taught: Rabban Simeon b. Gamaliel says: Wherever the Sages set their eyes there is either death or calamity
In other words, it seems that sight has power to cause damage. This source is not conclusive, but how about the story of Rabbi Shimon Bar Yochai when he and his son came out of the cave (Shabbat 33b):
נפקו חזו אינשי דקא כרבי וזרעי אמר מניחין חיי עולם ועוסקין בחיי שעה כל מקום שנותנין עיניהן מיד נשרף
So they emerged. Seeing a man ploughing and sowing, they exclaimed, 'They forsake life eternal and engage in life temporal!' Whatever they cast their eyes upon was immediately burnt up.
Similarly, when Rabbi Shimon saw Yehuda ben Gerim, who was the one who informed the Romans of his words the Gemara says (ibid. 34a)
נפק לשוקא חזייה ליהודה בן גרים אמר עדיין יש לזה בעולם נתן בו עיניו ועשהו גל של עצמות:
Then he went out into the street and saw Judah, the son of proselytes: 'That man is still in the world!' he exclaimed. He cast his eyes upon him and he became8 a heap of bones.
It seems that according to Chazal there is a fire that comes out of the eyes, which is normally weak, but when coupled with strong spiritual force it can become an actual fire and burn things up.
The truth is that I understand that the concept of ayin hara is also based on this worldview. I know that nowadays we tend to explain it as based on jealousy of others, but if so, why is there no concept of 'ozen hara'? It seems that actually looking at something has power to cause damage. Conversely there is a saying that:
וא"ר יצחק אין הברכה מצוייה אלא בדבר הסמוי מן העין
R. Isaac also said: A blessing is found only in what is hidden from the eye, for it is written, The Lord shall command the blessing upon thee in thy hidden things. The School of R. Ishmael taught: A blessing comes only to that over which the eye has no power, for it is said, The Lord shall command the blessing upon thee in thy hidden things.
All of these sources imply (to me) that the eye emits some force which can cause physical damage if not channeled properly.
(I know that Superman had similar powers - where do you think he got the idea from?)
Rashi in Chumash is explicit that this is how sight works. In parshat Haazinu (Devarim 32:10) the verse states:
יִמְצָאֵהוּ בְּאֶרֶץ מִדְבָּר וּבְתֹהוּ יְלֵל יְשִׁמֹן יְסֹבְבֶנְהוּ יְבוֹנְנֵהוּ יִצְּרֶנְהוּ כְּאִישׁוֹן עֵינוֹ
He found them in a desert land, and in a desolate, howling wasteland. He encompassed them and bestowed understanding upon them; He protected them as the pupil of His eye.
"כאישון עינו" - הוא השחור שבעין שהמאור יוצא הימנו"
as the pupil of his eye: This refers to the black part of the eye, from which the light comes outward.
I haven't yet found the source of Rashi's statement in Chazal. Perhaps one of you knows whether Rashi took this explanation from an earlier source, or it is his own chidush. Also I have looked, but not yet found, whether any of the commentaries on Rashi manage to explain this in accordance with modern theories of sight (i.e. that light comes from a light-source, is reflected off objects, and then enters the eye).
And what is also interesting is that both Rabbeinu Bachye (on the verse) and Meiri (in his commentary on Tehillim 17) seem to side with the other theory of sight, and say that the word ishun means pupil because of the 'little man' (ish) that can be seen within it. This seems to be the theory of eidola, that reflections leave the object and enter the eye. Again, I cannot find a source in Chazal for their commentary, but I would be glad if someone could find one for me.
It apears that the modern theory of sight first developed in the end of the 10th century and beginning of the 11th by Abu Ali Mohammed Ibn Al Hasn Ibn Al Haytham, whom we know today as Alhazen. However, since he lived mainly in Cairo, and wrote in Arabic, his works would have been unknown to Rashi, Rabbeinu Bachya or Meiri. But they should have been known to those who came not much later. Which is why I would expect later commentaries on Rashi (particularly) to explain him according to the 'modern theory.'