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The relative permeability of a liquid is 3/16, and the relative permittivity is 16. What is the refractive index of the liquid?

a. 3/16
b. 16/3
c. 4/3
d. 3/4

User INardex
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1 Answer

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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.

User Dmitry Gamolin
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