To calculate the material index, we can use the formula:
Material index = Speed of light in vacuum / Speed of light in the material
The speed of light in a vacuum is approximately 299,792,458 meters per second.
Given that a pulse of light takes 2.63 seconds to travel 0.500 meters in the material, we can determine the speed of light in the material as:
Speed of light in the material = Distance / Time = 0.500 m / 2.63 s
Now, we can calculate the material index:
Material index = Speed of light in vacuum / Speed of light in the material = 299,792,458 m/s / (0.500 m / 2.63 s) = 299,792,458 m/s / 0.1901140684410646 m/s ≈ 1,577,931,028.41878
Therefore, the material index is approximately 1,577,931,028.41878.