What is the relation between VG and VP?

Solution: The product of the phase and the group velocities is given by the square of the speed of the light. Thus Vp x Vg = c2 is the relation.

Is group velocity equal to phase velocity?

Group velocity and phase velocity are not necessarily the same. Group velocity is given by, Phase and group velocity are related through Rayleigh’s formula, If the derivative term is zero, group velocity equals phase velocity.

What is the formula for phase velocity?

For this reason, phase velocity is defined as v p = ω / k . This relation is generalized to three dimensions in Eq. (59). Given the phase velocity, the phase refractive index np is the factor describing how much slower the phase is propagating than the speed of light c0.

Which of the following is the correct relation between the group velocity Vg and phase velocity VP?

1 Answer. We have vp = ω/k or, ω = kvp.

What is the relation between the group and phase velocity of a relativistic free?

The product between the phase velocity and the group velocity of any particle (massive or massless) equals the square of the speed of light in vacuum. The group velocity of any particle (massive or massless) is equal to the derivative of its total relativistic energy with respect to its relativistic momentum.

Is phase velocity greater than group velocity?

For most substances, therefore, the group velocity is smaller than the phase velocity. In such cases, it is mathematically possible that the group velocity may be larger than the phase velocity.

What is the difference between phase velocity and group velocity *?

The main difference between Phase Velocity and Group Velocity is that phase velocity is greater than the group velocity in a normal medium.

What is group and phase velocity?

If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity. A wave of any shape will travel undistorted at this velocity. If ω is a linear function of k, but not directly proportional (ω = ak + b), then the group velocity and phase velocity are different.

What is the relation between phase velocity and wavelength?

For a constant frequency, the wavelength is directly proportional to velocity.

Is phase velocity is half of group velocity?

What is the phase and group velocity for a sinusoidally-varying wave in this material? Thus, we see that in this case the group velocity is always half the phase velocity. Another commonly-encountered example for which vg is not necessarily equal to vp is the propagation of guided waves; e.g., waves within a waveguide.

What is the relation between phase velocity and group velocity for a non relativistic free particle?

▶Relation between phase velocity and group velocity Thus for a non-relativistic free particle the group velocity (vg) is twice of the phase velocity (u).

In which medium the phase velocity and group velocity are not equal?

Detailed Solution. In a dispersive medium, the group velocity is less than the phase velocity only.

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