Final answer:
The distance light would have traveled in a vacuum can be calculated by determining the time it takes for light to travel through the ice and quartz and then converting that time into the equivalent distance in a vacuum.
Step-by-step explanation:
To find out how far light would have traveled in a vacuum in the time that it takes to travel through a flat sheet of ice and a flat sheet of crystalline quartz, we need to calculate the time taken for the light to pass through each material and then determine the equivalent distance in a vacuum.
The speed of light in a medium is given by c/n, where c is the speed of light in a vacuum and n is the refractive index of the medium.
For ice, with n = 1.309, the speed of light is c/1.309. The time taken to cross 1.9 cm is therefore thickness/speed = 1.9 cm / (c/1.309).
Similarly, for crystalline quartz, with n = 1.544, the speed of light is c/1.544. The time taken to cross 0.88 cm is 0.88 cm / (c/1.544).
The total distance light would have traveled in a vacuum is the sum of the distances covered in ice and quartz, calculated using their respective times. This is equivalent to c multiplied by the total time (the sum of the individual times for ice and quartz).