This page provides solution to the puzzle with prisms that you encounter in the seventh chapter of Uncharted: The Lost Legacy. The premise of the puzzle is that you manipulate interactive statues, so that light reflects from the mirrors and light successive fragments of the large chamber. After you solve the battle, you will also have to fight some enemies, but this is not too difficult.
After you have used hook and rope to reach another part of the large cave, approach the first statue with a prism atop. Rotate it several times in any direction, step back and wait for the conversation icon appear over Nadine's head. Have another optional conversation (3/3).
After that, take to the puzzle. You have to rotate the statue for the prism to reflect sunbeams at the right angle and light another one shown in the above screenshot, located to the left of the starting point (the beams are also reflected by the prism of the first statue, but you will explore that area later on).
Head towards are to the left of where you have started the puzzle (you can use hooks to change places faster). Ignore the second statue for now and reach the third one shown in screenshot 1. You can move that statue in a straight line, on rails. Make it stop under the mirror under the ceiling shown in screenshot 2.
Return to the second statue now and rotate it to reflect the beam towards the one on the rails (what's interesting, you can have Nadine do that by letting her rotate the second statue).
At this stage of the puzzle, the beam should reflect from the third statue and from the mirror inside the hanging cage in the center (the one you used to get here). The current setting has been shown in the above screenshot.
Head towards the area to the right of the starting point, i.e. the one that you have not yet explored. Reach the spot where there is a destroyed statue, shown in the above screenshot. Examine it and Nadine will offer to stand in for the statue and hold up the mirror. Do not walk away too far, because right after Nadine holds up the mirror, you will get another photo opportunity location (7/7) (Chloe will photo Nadine holding up the mirror).
You can now go towards the statue on rails and with mirror, in the distance. Move it to the position shown in the above screenshot, thanks to which the mirror will reflect the beam towards the ceiling. This way, you will have solved the puzzle.
A cutscene will start and, right after you see it, you will have to leave this location and eliminate all the Asav's men in your way. You will run into the first larger group right after you turn left. Watch out for the opponents with shotguns and eliminate them with grenades and C4 charges, if you have them.
Another, larger group will appear in the location shown in the above screenshot and this is going to be more difficult, because of a partially collapsed balcony. Continue your journey and deal with an even larger group of opponents. The fight will end in a longer cutscene, in which the protagonists will be captured by Asav.