Final answer:
The index of refraction of a material where light's wavelength is 0.671 times its value in a vacuum is approximately 1.49. The likely substance with this index of refraction is water, so the correct answer is a) 1.49 (Water).
Step-by-step explanation:
The question asks about the index of refraction (n) of a material where the wavelength of light is 0.671 times its value in a vacuum. By definition, the index of refraction is the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v). In mathematical terms, it is expressed as n = c / v. When the wavelength of light in a material is a fraction of its wavelength in a vacuum, it can be related to the index of refraction using the equation n = λ0 / λ, where λ0 is the wavelength in a vacuum and λ is the wavelength in the material.
Given that the wavelength in the material is 0.671 times the wavelength in a vacuum, we find that n = 1 / 0.671, which equals approximately 1.49. The substances given as options are water (n = 1.49), air (n = 1.33), diamond (n = 2.00), and vacuum (n = 1.00). Since our calculated index of refraction is 1.49, we can conclude that the likely substance is water. Thus, the correct option is a) 1.49 (Water).