Question

The velocity of light through a medium of relative permittivity 2 and relative permeability 4.5 is (in terms of $ c $):

• A. \( \frac{c}{\sqrt{2 \cdot 4.5}} \)
• B. \( \frac{c}{\sqrt{2 \cdot 4}} \)
• C. \( \frac{c}{\sqrt{2 \cdot 5}} \)
• D. \( \frac{c}{\sqrt{4.5}} \)

Hint:

When working with the velocity of light in different media, remember that the speed depends on both the relative permittivity and the relative permeability of the medium. Use the formula \( v = \frac{c}{\sqrt{\epsilon_r \mu_r}} \) to calculate the velocity.

Answer 1

The Correct Option is A

The velocity of light in a medium with relative permittivity \( \epsilon_r \) and relative permeability \( \mu_r \) is given by: \[ v = \frac{c}{\sqrt{\epsilon_r \mu_r}} \] Where: 
- \( c \) is the velocity of light in vacuum, 
- \( \epsilon_r \) is the relative permittivity, 
- \( \mu_r \) is the relative permeability. We are given that the relative permittivity \( \epsilon_r = 2 \) and the relative permeability \( \mu_r = 4.5 \). Substitute these values into the formula: \[ v = \frac{c}{\sqrt{2 \cdot 4.5}} \] Now, simplifying the expression: \[ v = \frac{c}{\sqrt{9}} = \frac{c}{3} \] 
Thus, the velocity of light in this medium is \( \frac{c}{\sqrt{2 \cdot 4.5}} \). So the correct answer is (A) \( \frac{c}{\sqrt{2 \cdot 4.5}} \).