Final answer:
Option D: To find the refractive index of a liquid, we use the formula n = √(μ_r × ε_r). With μ_r = 3/16 and ε_r = 16, we get n ≈ 1.732. Thus, when rounded, the refractive index is approximately 3/4, which corresponds to answer choice (d).
Step-by-step explanation:
The refractive index of a substance can be found using the relative permeability (μ_r) and relative permittivity (ε_r), and their relationship with the speed of light in that medium. The formula used is n = √(μ_r × ε_r), with 'n' being the refractive index. In this case, the relative permeability is 3/16 and the relative permittivity is 16. By plugging these values into the formula, we get:
n = √((3/16) × 16) = √(3) ≈ 1.732
Therefore, the correct answer is (d) 3/4 when rounded up to two decimal places.
The refractive index of a substance can be determined using the formula:
Index of refraction (n) = Speed of light in vacuum / Speed of light in the substance.
Given the relative permeability of the liquid is 3/16 and the relative permittivity is 16, we can determine the refractive index.
Refractive index (n) = sqrt(relative permeability * relative permittivity)
Refractive index (n) = sqrt(3/16 * 16) = sqrt(3/1) = sqrt(3) = 1.732
Therefore, the refractive index of the liquid is approximately 1.732.