The refractive indices of materials A and B have a ratio of nA/nB = 1.38. The speed of light in material A is 1.25 108 m/s. What is the speed of light in material B?
I bet the speed of light in B is faster by a factor of 1.38.
Isn't index of refraction inversely related to speed of light in the medium
To find the speed of light in material B, we can use Snell's law which relates the refractive index and the speed of light in different materials.
Snell's law states that the ratio of the speed of light in a vacuum (c) to the speed of light in a material (v) is equal to the ratio of the refractive indices of the two materials:
c / v = nA / nB
Given that the ratio of the refractive indices is nA/nB = 1.38, and the speed of light in material A is vA = 1.25 * 10^8 m/s, we can rearrange Snell's law to solve for the speed of light in material B:
vB = c / (nA / nB)
Plugging in the values, we have:
vB = (3.00 * 10^8 m/s) / (1.38)
Calculating the result:
vB ≈ 2.17 * 10^8 m/s
Therefore, the speed of light in material B is approximately 2.17 * 10^8 m/s.