Final answer:
To find the index of refraction of the gas in a cube during a lab experiment, one must measure how light is refracted through the gas compared to the known plastic material of the cube and apply Snell's Law to solve for the unknown index.
Step-by-step explanation:
When working with a plastic cube that has a hollow cube-shaped space in the middle, to determine the index of refraction of a gas that fills this space, you need to collect specific data during a lab experiment. Firstly, you would need to know the index of refraction of the plastic material of the cube. Since the index of refraction is the ratio of the speed of light in a vacuum to the speed of light in the material, having the value for the plastic allows for a comparison. With the plastic's index already known, students would need to perform experiments that measure how light is bent or refracted when it passes through the plastic cube and then the gas-filled space. This could involve directing a laser or light source through the cube and measuring the angle of incidence and the angle of refraction.
After collecting the refraction angle data, students can apply Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media. This will enable students to solve for the unknown index of refraction of the gas contained within the hollow space of the cube. Understanding how to calculate square roots or cube roots might be necessary depending on the mathematical relationship that arises in the analysis.