Question

An electromagnetic wave travelling in a medium has its electric field given by : \(E = 2\sin(2 \times 10^{15}t - 10^7x)\). Find the refractive index of the medium :

• A. 1.1
• B. 1.7
• C. 1.3
• D. 1.5

Hint:

Always look for the coefficients of \(t\) and \(x\). Their ratio (\(t/x\)) gives the phase velocity \(v\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Refractive index (\(\mu\)) is the ratio of the speed of light in vacuum to the speed of light in the medium.
Step 2: Key Formula or Approach:
1. Standard wave equation: \(E = E_0 \sin(\omega t - kx)\).
2. Speed of wave: \(v = \frac{\omega}{k}\).
3. Refractive index: \(\mu = \frac{c}{v}\).
Step 3: Detailed Explanation:
From the given equation:
\(\omega = 2 \times 10^{15} \text{ rad/s}\)
\(k = 10^7 \text{ m}^{-1}\)
Speed of wave in the medium:
\[ v = \frac{\omega}{k} = \frac{2 \times 10^{15}}{10^7} = 2 \times 10^8 \text{ m/s} \]
Speed of light in vacuum: \(c = 3 \times 10^8 \text{ m/s}\).
Refractive index:
\[ \mu = \frac{c}{v} = \frac{3 \times 10^8}{2 \times 10^8} = 1.5 \]
Step 4: Final Answer:
The refractive index of the medium is 1.5.