Question

The refractive index of a material is defined as:

• A. Ratio of velocity of light in vacuum to velocity in material
• B. Ratio of permittivity to permeability
• C. Absorption coefficient of light
• D. Polarization per unit field

Hint:

Since light always travels slower in a physical medium than in a vacuum ($v < c$), the absolute refractive index for any real material is always greater than or equal to 1 ($n \ge 1$).

Answer 1

The Correct Option is A

Concept: The refractive index ($n$) of an optical medium is a dimensionless parameter that describes how light propagates through that medium. It is an indicator of the optical density of the material and determines how much the path of light bends (refracts) when entering the medium from a vacuum or air, governed by Snell's Law. Maxwell's electromagnetic equations state that the phase velocity of light in any medium is restricted by its fundamental electromagnetic properties: \[ v = \frac{1}{\sqrt{\epsilon \mu}} \] Where $\epsilon$ is the absolute permittivity and $\mu$ is the absolute permeability of the medium.

Step 1: Setting up the standard ratio for refractive index.
By absolute definition, the refractive index ($n$) compares the speed of an electromagnetic wave in a pristine vacuum ($c$) against its slowed-down phase velocity ($v$) inside the physical medium: \[ n = \frac{c}{v} \] In a vacuum, the velocity is at its physical maximum: \[ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \] Where $\epsilon_0$ is the vacuum permittivity and $\mu_0$ is the vacuum permeability.

Step 2: Connecting the definition with electromagnetic parameters.
Substituting the velocity expressions into our ratio equation yields: \[ n = \frac{\frac{1}{\sqrt{\epsilon_0 \mu_0}}}{\frac{1}{\sqrt{\epsilon \mu}}} = \sqrt{\frac{\epsilon \mu}{\epsilon_0 \mu_0}} = \sqrt{\epsilon_r \mu_r} \] Where $\epsilon_r$ is the relative permittivity (dielectric constant) and $\mu_r$ is the relative magnetic permeability. For non-magnetic materials, $\mu_r \approx 1$, meaning $n \approx \sqrt{\epsilon_r}$. This confirms that the fundamental definition is based strictly on the ratio of velocities described in option (A).

Step 3: Checking the other definitions.

• Option B: The ratio $\sqrt{\mu/\epsilon}$ defines the characteristic wave impedance ($Z$) of the medium, not the refractive index.
• Option C: The absorption coefficient measures optical attenuation per unit length due to energy dissipation.
• Option D: Polarization per unit field defines electric susceptibility ($\chi_e$), which relates to charge displacement under an electric field. Therefore, option (A) is the only correct definition.