Final answer:
To calculate the index of refraction of a medium with a wave frequency of 5.1 • 10⁾¹⁴ Hz and a wave speed of 2.1 • 10⁸ m/s, use the formula n = c/v. With c as the speed of light in a vacuum (approximately 3.00 • 10⁸ m/s), the index of refraction, n, is approximately 1.43.
Step-by-step explanation:
The student has asked about calculating the index of refraction for a medium given the frequency and speed of a wave in that medium. The index of refraction, represented by the symbol n, is calculated using the formula n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. First, we need to acknowledge that the frequency of the wave (f) does not directly affect the index of refraction but it is related to wavelength (λ), which is needed when assessing wave properties. Since the frequency given is 5.1 • 1014 Hz, and the speed of light in a vacuum is approximately c = 3.00 • 108 m/s, we need only the speed of the wave in the medium (v = 2.1 • 108 m/s) to find the index of refraction. By plugging the known values into the formula, the index of refraction n can be calculated:
n = c/v = (3.00 • 108 m/s) / (2.1 • 108 m/s) = 1.43
Therefore, the index of refraction of the medium is approximately 1.43.