The Question is from NEET guide , and it was created by the author SUBHANI

Question

If ${\varepsilon _0}$ and ${\mu _0}$ represent the permittivity and permeability of vacuum and $\varepsilon $ and $\mu $ represent the permittivity and permeability of medium, then refractive index of the medium is given by

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Refractive Index and its relation to permittivity and permeability.
	**Related Topics**: Speed of light in a medium, Electromagnetic waves.
	**Prerequisites**: Understanding of permittivity, permeability, and the relationship between speed of light and these properties.
## SOLUTION PATHWAY
**Given Information**:
	- Permittivity of vacuum: ${\varepsilon _0}$
	- Permeability of vacuum: ${\mu _0}$
	- Permittivity of medium: $\varepsilon$
	- Permeability of medium: $\mu$
**Method & Steps**:
	1. **Recall the speed of light in vacuum (c) and a medium (v):**
		Reasoning: Speed of light is related to permittivity and permeability by the following formulas.
		Formula/Rule: $c = \frac{1}{\sqrt{{\mu _0}{\varepsilon _0}}}$ and $v = \frac{1}{\sqrt{{\mu \varepsilon}}}$
	2. **Recall the definition of refractive index (n):**
		Reasoning: Refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium.
		Formula/Rule: $n = \frac{c}{v}$
	3. **Substitute the expressions for c and v into the refractive index formula:**
		Working: $n = \frac{\frac{1}{\sqrt{{\mu _0}{\varepsilon _0}}}}{\frac{1}{\sqrt{{\mu \varepsilon}}}} = \frac{\sqrt{{\mu \varepsilon}}}{\sqrt{{\mu _0}{\varepsilon _0}}} = \sqrt{\frac{{\mu \varepsilon}}{{\mu _0}{\varepsilon _0}}}$
		Key Point: The refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium.
	4. **Final Result:**
		Result: $n = \sqrt{\frac{{\mu \varepsilon}}{{\mu _0}{\varepsilon _0}}}$
		Verification: The result matches option B.
## OPTION ANALYSIS
[A] :x: This option has the inverse ratio of permittivity and permeability.
[B] ✓: This option correctly represents the refractive index based on the given parameters.
[C] :x: This option only includes permeability and not permittivity of the medium.
[D] :x: This option has the inverse ratio with only permeability term in denominator.
## LEARNING AIDS
	**Common Mistakes**:
		1. **Inverting the ratio**: Confusing the numerator and denominator in the refractive index formula.
			How to avoid: Remember that refractive index is the ratio of speed of light in vacuum to speed in the medium.
		2. **Mixing up permittivity and permeability**: Forgetting which parameter goes where in the speed of light formulas.
			How to avoid: Remember that both permittivity and permeability are under the square root in the formula for the speed of light.
	**Quick Tips**:
		1. **Remembering the formula**: The refractive index is a ratio of two speeds of light and can be remembered by its relation to the permittivity and permeability.
		2. **Units**: Always check units to understand which formula to use.

SUBHANI · Answer

$\sqrt {\frac{{{{\rm{\mu }}_0}{{\rm{\varepsilon }}_0}}}{{{\rm{\mu \varepsilon }}}}} $

SUBHANI · Answer

The correct Option is "$\sqrt {\frac{{{\rm{\mu \varepsilon }}}}{{{{\rm{\mu }}_0}{{\rm{\varepsilon }}_0}}}} $"

SUBHANI · Answer

$\sqrt {\frac{{\rm{\mu }}}{{{{\rm{\mu }}_0}{{\rm{\varepsilon }}_0}}}} $

SUBHANI · Answer

$\sqrt {\frac{{{{\rm{\mu }}_0}{{\rm{\varepsilon }}_0}}}{{\rm{\mu }}}} $

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