The distinguished glasses are one of two items that Soichiro Shimoda treasures, and requests for Nana Ogasawara, Chihaya Yamase and Nari Amatoya to help him find. It's the first of his items to be found.
After solving a brief puzzle and figuring out that the other glasses are not his, the three girls head toward the second floor of the main building. There, they come across three red spirits who tell them lies about the location of the glasses. They eventually go to the stairwell leading to the first floor, and find the glasses on one of the railings.
Once they return the glasses to Soichiro, he is grateful.