Question

A radio wave travels in a medium with refractive index 1.5. What is the speed of light in this medium if the speed of light in vacuum is \(3 \times 10^8 \, \text{m/s}\)?

• A. \(2 \times 10^8 \, \text{m/s}\)
• B. \(1.5 \times 10^8 \, \text{m/s}\)
• C. \(2.5 \times 10^8 \, \text{m/s}\)
• D. \(1.6 \times 10^8 \, \text{m/s}\)

Hint:

Use the relation \( v = \frac{c_0}{n} \) to find the speed of light in any medium.

Answer 1

The Correct Option is A

The speed of light in a medium is related to the speed of light in vacuum \(c_0\) and the refractive index \(n\) by the formula: \[ v = \frac{c_0}{n}, \] where: - \(c_0 = 3 \times 10^8 \, \text{m/s}\) (speed of light in vacuum), - \(n = 1.5\) (refractive index of the medium), - \(v\) is the speed of light in the medium. Substituting the values: \[ v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \, \text{m/s}. \] Thus, the speed of light in the medium is: \[ \boxed{2 \times 10^8 \, \text{m/s}}. \]