Prove that the group velocity vg of electromagnetic waves in dispersive medium with refractive index n is given by

where c is the free-space velocity of light and w is the angular frequency of the waves. A pulsar is a star which emits very sharp pulses over a broad range of radio frequencies. These travel through the interstellar medium in a straight line before arriving at Earth. Radio observations show that the arrival time of a particular pulse measured at 400 MHz is 700 later than the arrival time of the same pulse measured at 1400 MHz. The refractive index of the interstellar medium is given by

n² = 1 ? Ne²/?₀mw²

where e and m are the charge and mass of an electron, and N is the electron density, which is known to have an approximately uniform value of 3 x 10⁴ m?3 in the space between the Earth and the pulsar. Calculate the distance to the pulsar.

Transcribed Image Text:

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