How do you find refractive index and group velocity?

For light propagating in a waveguide such as an optical fiber, the group velocity can be calculated by replacing the wavenumber k with β (the imaginary part of the propagation constant) (or replacing the refractive index n with the effective refractive index) in the equation given above.

What is phase velocity group velocity?

Waves can be in the group and such groups are called wave packets, so the velocity with a wave packet travels is called group velocity. The velocity with which the phase of a wave travels is called phase velocity.

How is the group velocity related to the refractive index?

For light, the refractive index n, vacuum wavelength λ0, and wavelength in the medium λ, are related by with vp = ω/k the phase velocity . The group velocity, therefore, can be calculated by any of the following formulas,

How is the phase velocity related to the frequency?

In a given medium, the frequency is some function ω(k) of the wave number, so in general, the phase velocity v p = ω/k and the group velocity v g = dω/dk depend on the frequency and on the medium. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c/v p = ck/ω.

How is the refractive index of a medium calculated?

The index of refraction is equal to the speed of light in a medium divided by the speed of light in a vacuum. . Plug in the given values and solve for the velocity in the medium. . We can recognize that the answer can be simplified by converting to nanoseconds. The refractive index of medium A is 1.2, while that of medium B is 1.36.

How to calculate the group velocity of light?

For light, the refractive index n, vacuum wavelength λ0, and wavelength in the medium λ, are related by with vp = ω/k the phase velocity . The group velocity, therefore, can be calculated by any of the following formulas, v g = c n + ω ∂ n ∂ ω = c n − λ 0 ∂ n ∂ λ 0 = v p ( 1 + λ n ∂ n ∂ λ ) = v p − λ ∂ v p ∂ λ = v p + k ∂ v p ∂ k .