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If μᵣ be relative permeability and K be the dielectric constant of a given medium then the refractive index of the medium is n= ________.

Asked in GSEB Board July 2016 · Refractive index and dielectric constant

• (1) √μᵣ ε₀
• (2) √μᵣ K
• (3) 1/(√μᵣ K)
• (4) √(μᵣ)/K

Step-by-step solution

Why the other options are wrong

• (1) comes from mixes a relative quantity with an absolute one. μᵣ is a pure number but ε₀ is not, so this expression is not even dimensionless, while a refractive index must be.
• (3) comes from is the answer turned upside down. 1/(√μᵣ K) is v/c, which is less than 1 for any ordinary medium, whereas n is greater than 1.
• (4) comes from divides by K instead of multiplying. Then a medium with a large dielectric constant would come out with a small refractive index, which is the opposite of what happens.

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