Final answer:
The index of refraction needed to slow light down to 210 m/s would be 1.428571 × 106, an unrealistically high number since no known material has such a high index of refraction, making it practically impossible to achieve.
Step-by-step explanation:
To calculate the index of refraction for a material that would slow light down to the speed of a commercial jet airliner, which is 210 m/s, we can use the formula for the index of refraction (n), which is the speed of light in a vacuum (c) divided by the speed of light in the material (v):
n = c / v
The speed of light in a vacuum (c) is approximately 3.00 × 108 m/s. Plugging in the values, we get:
n = 3.00 × 108 m/s / 210 m/s
Calculating this, we find:
n = 1.428571 × 106
Thus, the index of refraction required to slow light down to 210 m/s is extraordinarily high and is not realistic as no known material has such a high index of refraction. In practice, light cannot be slowed down to the speed of a commercial jet airliner through any known transparent material.