Question

The refractive index of medium is 1.8 and its relative permeability is 2.16. The relative permittivity of the medium is (nearly):

• A. 1.5
• B. 1.6
• C. 1.4
• D. 1.7

Hint:

The refractive index in relation to the electromagnetic properties of a medium offers insights into its interaction with light and other electromagnetic waves.

Answer 1

The Correct Option is A

We are given: 
- The refractive index of the medium, \( n = 1.8 \), 
- The relative permeability of the medium, \( \mu_r = 2.16 \). 
The refractive index \( n \) is related to the relative permittivity \( \epsilon_r \) and the relative permeability \( \mu_r \) by the formula: \[ n = \sqrt{\epsilon_r \mu_r} \] 
where: 
- \( \epsilon_r \) is the relative permittivity, 
- \( \mu_r \) is the relative permeability. 
Substitute the given values into this equation: \[ 1.8 = \sqrt{\epsilon_r \times 2.16} \] Squaring both sides: \[ 3.24 = \epsilon_r \times 2.16 \] 
Now, solving for \( \epsilon_r \): \[ \epsilon_r = \frac{3.24}{2.16} \approx 1.5 \] Thus, the relative permittivity of the medium is approximately \( 1.5 \). 
Conclusion: The relative permittivity of the medium is nearly 1.5, so the correct answer is Option (1).