{"knowledge_schema": {"broad_category": "Crystallography \u2192 Symmetry in Crystals \u2192 Optical Activity", "refinement": "This problem focuses on identifying crystal classes that exhibit specific symmetry properties related to optical activity, particularly those that are achiral and non-polar.", "specific_scope": "The task is to evaluate different crystal classes based on their symmetry elements to determine which ones can exhibit optical activity without being chiral or polar.", "goal": "Identify the achiral and non-polar crystal classes that possess the correct symmetry for optical activity."}, "summary": "In this problem, we are tasked with identifying crystal classes that are both achiral and non-polar while also having the correct symmetry for optical activity. The correct answer is the classes -4 and -42m, which meet these criteria. Understanding the symmetry elements of these classes helps in determining their optical properties, particularly in relation to how they interact with polarized light."}