Question

In vacuum the speed of light depends upon

Answer 1

No the speed of light in a vacuum does not depend on frequency (or wavelength). When light travels through any medium other than a vacuum, its speed is lower than in the vacuum. When travelling through some media, it can be that the speed of light will be different for different wavelengths
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Answer 2

Answer:

No the speed of light in a vacuum does not depend on frequency (or wavelength).  

When light travels through any medium other than a vacuum, its speed is lower than in the vacuum.  When travelling through some media, it can be that the speed of light will be different for different wavelengths.  That is called dispersion (because the different parts of the light disperse, or spread out, as they travel along).  But vacuum is not dispersive, so light of all wavelengths travel at the same speed.  

The frequency depends on the conditions where the light was emitted.  Strangly, the frequency can change as it propagates through gravity fields (as the light gains or loses energy).  

Where nu is the frequency (See: Photon).

But the speed travelling through a vacuum is always the same.  

The wavelength and frequency go hand-in-hand such that frequency times wavelength equals speed of light in whatever medium the light is travelling through.

Explanation: