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I was studying the prism and how and why it disperses light. My teacher told me that in a prism different wavelengths of light have different refractive indexes because the refractive index depends upon the wavelength of light and also because the wavelength of different colors of light are different, light of different colors travel with different speeds.

The question is why does then the speed of different colors of light not different in air or vaccum if it is how come we observe white light? Also, because the frequency depends on the source and wavelength of each color is different the speed should be different because

$$ v = f\lambda $$ and frequency depends on the source. Is there any other way in which the speed of different colors of light are controlled?

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    $\begingroup$ Air actually IS dispersive but the refractive index for visible light (~300-800 nm) is so close to one that people usually approximate it to one. $\endgroup$
    – Yababaa
    Commented Dec 27, 2022 at 18:30

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It does. Dispersion dynamics in optics,- ${dn}/{d\lambda}$ is qualified by Abbe number, which is defined by contrasting refractive indexes at Fraunhofer spectral lines : $$ V_{D}={\frac {n_{d}-1}{n_{F}-n_{C}}}. \tag 1$$

For air $$V_D = \frac {1.00027717−1}{1.00027936−1.00027625} \approx 89 \tag 2,$$

which is comparable to some fluorite and phosphate crown glasses, having Abbe numbers in range $[75 - 85].$

And here's air dispersion chart in a visible EM spectrum ($0.4-0.7 \mu m$):

enter image description here

As a side note, flint glasses used in lens, Abbe number is about $50$. So air dispersion is about $1.78 \times$ lower than that in flint glass. (Higher Abbe number corresponds to lower dispersion characteristics.)

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