How is the narrator finally able to see the dimensions of his chamber? What mistake does he realize he made about the size of the chamber?
After the narrator is deposited into the pit, he does not immediately open his eyes. When he does, he sees nothing but darkness. So, he sees nothing. He makes his way around the chamber but he can not measure the circumference or perimeter because he has no way to know when he has come back to the place he has started. He uses a piece of his clothing to mark a spot and, coming back to it, he estimates that the chamber is fifty yard "in circuit" (circumference).
He falls and realizes that there is a pit in the middle of the chamber. To estimate the depth, he drops a fragment (piece of rock, perhaps) and eventually hears it drop into the water. Then he hears the sound of a door opening overhead, and a faint beam of light comes in briefly. This enables him to see for a brief moment:
At the same moment there came a sound resembling the quick opening, and as rapid closing of a door overhead, while a faint gleam of light flashed suddenly through the gloom, and as suddenly faded away.
He drinks again from a pitcher and passes out. When he wakes up, there is a greater amount of light but he can not see the origin of the light. This is when he is able to really see the dimensions of the room. He realizes that the circuit (which he thought was 50 yards) is less than 25 yards. He had also thought the shape of the room was irregular, but upon seeing it, the room is basically square. He sees all of this from his new position of being strapped to a piece of wood on his back.