To determine if a solution is optically dilute or thick, the absorption coefficient (a) is key, as it indicates how much light is absorbed per centimeter. A lower absorption coefficient suggests an optically dilute solution, while a higher coefficient indicates an optically thick solution. The relationship between transmitted intensity (I) and incident intensity (Io) can be expressed using the equation I = Io e^(-ax), allowing for calculations of a based on light transmission percentages. For example, when 75% of light is transmitted, a equals 0.28, while at 50% and 25% transmission, a equals 0.69 and 1.39, respectively. Understanding these values can help assess the optical properties of various solutions.