In "Lord of the Flies", what is the connection between Ralph, the conch, and the glasses?
I think the main connection is about the idea of democracy and fairness they represent.
Ralph, as chief, represents an idea of democracy and fairness. It's significant, I think, that in the first chapter, when Ralph is elected chief, it is a democratic election and the conch, as a symbol of togetherness, influences the boys' vote: they vote for Ralph because...
...most obscurely, yet most powerfully, there was the conch. The being that had blown that, had sat waiting for them on the platform with the delicate thing balanced on his knees, was set apart.
“Him with the shell.”
“Let him be chief with the trumpet-thing.”
And then, in the second chapter, it's the conch that becomes the symbol of who can speak, of everyone listening to a single speaker. The conch initially summoned all the boys together: and it now represents keeping them together, a sign of "order, authority, dialogue, democracy":
"That’s what this shell’s called. I’ll give the conch to the next person to speak. He can hold it when he’s speaking.”
Ralph as chief is chiefly bothered about the fire. It's important, he realises, to have the fire as a signal so that they might be rescued. And this fire needs Piggy's glasses to be lit. The glasses, then are literally and metaphorically associated with clear-sightedness - like Ralph's insistence on the fire.
So you see the link. Ralph, the conch, and the glasses are all tied into Ralph's ideas as chief - the opposite to Jack, hunting, and sharpened sticks!
The conch shell represents "order, authority, dialogue, democracy." Ralph then becomes their chosen leader. In fact, he was the one who pointed the conch shell out when they first arrived at the island; however, it was Piggy who pointed out how to use it to make an announcement or to call for help.
While the shell stands for those qualities, Ralph doesn't necessarily fit that bill. He is able to get along with the different types of boys and he is also able to read each of them with his powers of observation. Another leader-type quality that Ralph possesses is that he is honestly concerned for each and every one of the boys on the island. He does care for them and wants them all to remain safe.
The glasses on the other hand belong to Piggy. He represents the intelligence of the island. He owns the glasses because he is able to truly see people and their ideas for what they really are. Ralph can do these things as well, but he ahs to have Piggy's help in doing so. Once Jack's tribe steals the glasses away from Ralph and Piggy, Ralph loses his ability to see things clearly. Ralph ties in with these two objects as closely as he ties in with Piggy. He is the leader (conch= authority), but he doesn't have the wisdom and common sense that Piggy has (that is represented by the glasses). He has it in the beginning, but after losing the specs, he is unable to remember some of the important things.