Relation bw speed of light and wavelength

[SonhosDaVida]

Are lights with a longer wavelength always at a higher speed than lights of a shorter wavelength of traveling thru the same medium?

TBR question stated that index of refraction is inversely proportional to the wavelength and since the wavelength is directly proportional to the velocity, light waves with higher wavelength travel faster. This was in the context of visible light waves.

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[PositivePhotoresist]

Yes!

Define l as wavelength in a new medium and lo as wavelength in a vacuum. We have: lo/l = (c/f)/(v/f) = c/v = n. Experimentally, we know that the frequency of the light doesn’t change when shifting mediums. I recommend googling some of the math supporting the observation because it’s quite cool.

Note: Be careful about which medium you’re in when doing these questions.