Final answer:
To find the distance light would have traveled in a vacuum while passing through crystalline and fused quartz, one must divide the thicknesses of each material by their respective refractive indices and sum the results.
Step-by-step explanation:
The student's question involves calculating the equivalent distance light would travel in a vacuum if it passes through two different materials with specific thicknesses. To solve this, we need to know the refractive indices of both materials and the thicknesses provided. For crystalline quartz with a refractive index of 1.544 and a thickness of 2.31 cm, and fused quartz on a thickness of 1.06 cm (assuming its refractive index to be around 1.46, a common value for fused quartz), we can apply the formula L = t/n, where L is the distance light would travel in a vacuum, t is the thickness of the material, and n is the refractive index of the material.
For crystalline quartz: Lcq = 2.31 cm / 1.544
For fused quartz: Lfq = 1.06 cm / 1.46
Adding these distances together gives us the total distance Ltotal light would travel in a vacuum in the time it takes to pass through both quartz layers.