Skyrim Secondaries Intersection- Saarthal: It's a Trap

Putter about a bit and you can turn up some more supplies and a vein of iron ore before heading down a tunnel leading deeper into the ruins.  Here there is another vein of iron ore, and an intersection where one turn is a dead-end, and the other leads to a balcony in a large room.  Follow the balcony, keeping to the outward edges, and you can make a couple of leaps that will get you a chest from one location and some mushrooms and leather strips from another.

Descend the ramp here and you can scrum the room for more alchemical supplies and a vein of gold ore.  Make note of the stone bridge leading to a passage in the wall, but don't use it until you've gathered everything of value that you can reach within the room.

Once you're ready, cross the bridge and enter the West passage.  Tolfdir is here, and he warns you to be cautious as you pass, since they haven't made sure of the site beyond this point.  Arniel Gane, the man you've been told to help, is standing at a table in the left branch of the corridor, so go and talk to him.

He directs you to look around to the North for some artifacts- your quest markers will note those as several enchanted rings lying around on the floor.  Don't forget to grab the soul gem off a nearby bookshelf as you go, and ensure that the last thing you grab is the Ancient Amulet hanging on the wall by the lowered porticullis.

Grabbing the amulet, unfortunately for you, lowers a pair of gates behind you, blocking you off from the entrance and your teacher!

Approach Tolfdir, who exclaims in concern as you explain that you've been trapped as a result of your taking the amulet.  He suggests finding a way to use the amulet in order to escape the trap.  Being an amulet, its uses are rather limited, so put it on and a glow will start from the area of the wall where you found the amulet.  Tolfdir sees this too, and wonders aloud what your spells might do- so cast whatever Destruction spell you can manage on the chunk of wall.  This blasts it away, opening a new passage in addition to removing the gates cutting you off from the earlier parts of the ruin.

Tolfdir now heads for the newly opened area- take this opportunity to give Arniel the three rings you found on the floor and then follow your teacher deeper into the ruins.

Unsure of what may be found here, Tolfdir pauses as you enter a room with a small podium and tells you to be on your guard for whatever may occur next.