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Let us list some of the factors which could possibly influence the speed of wave propagation : (i) Nature of source (ii) direction of propagation (iii) motion of source and//or observer (iv) wave length (v) intensity of the wave.
On which of these factors, if any does (a) the speed of light in vaccum (b) speed of light in a medium (say glass or water) depend ?

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(a) Thespeed of light in a vacuum `i.e.,3xx10^(8) m//s` (approximately) is a universal constant.It is not affected by the motion of the source, the observer, or both. Hence, the given factor does not affect the speed of light in a vacuum.
(b) Out of the listed factors, the speed of light in a medium depends on the wavelength of light in that medium.

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