Question

Which of the following conditions will lead to Anomalous dispersion?

• A. Group velocity>Phase Velocity
• B. Group velocity<Phase Velocity
• C. Group velocity = Phase Velocity
• D. Doesn't depend on relation of group and phase velocity

Hint:

A simple way to remember is: - Normal: \(v_g<v_p\) (The "normal" situation for light through a prism). - Anomalous: \(v_g>v_p\) (The "anomalous" or unusual case). - Non-dispersive: \(v_g = v_p\) (e.g., light in a vacuum).

Answer 1

The Correct Option is A

Step 1: Define dispersion. Dispersion is the phenomenon where the phase velocity of a wave depends on its frequency. The relationship is characterized by group velocity (\(v_g = \frac{d\omega}{dk}\)) and phase velocity (\(v_p = \frac{\omega}{k}\)).
Step 2: Characterize the types of dispersion. - **No Dispersion:** The phase velocity is constant for all frequencies. In this case, \(v_g = v_p\). - **Normal Dispersion:** The phase velocity decreases as frequency increases (e.g., light in glass). This corresponds to \(v_g<v_p\). - **Anomalous Dispersion:** The phase velocity increases as frequency increases. This phenomenon occurs in specific frequency bands, typically near a medium's absorption frequency. This condition corresponds to \(v_g>v_p\). Therefore, anomalous dispersion occurs when the group velocity is greater than the phase velocity.