In the vacuum the speed of light is the same, for all colors that are part of the white light. However each color differs by its value of frequency and wavelength.
The color violet is the component of white light with greater frequency and lower wavelength within the spectrum of visible light. A photon of light violet has the following values for the frequency and wavelength:
f = 7.5*10^14 s^-1
λ = 0.4*10^-6 m
According to these values, the speed of a photon of violet light in vacuum is:
v = λ*f = (0.4*10^-6)(7.5*10^14)
v = 3*10^8 m/s
So, from the equation for the speed we can find the distance d, traveled by the photon during 4.2 ns:
v = d/t → d = v*t
d = (3*10^8)(4.2*10-9)
d = 12.6*10^-1 = 1.26 m
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