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I was surprised to see my textbook having the following: "The focal length of a lens does not change when Red light is replaced by Blue light"- as an incorrect statement.

Why would the focal length change? From my knowledge it only depends on $\mu $ (refractive index of the material of lens and also of the medium) and the radius of curvature of lens following the lens maker equation? So how would that change on changing the light frequency ?

I realize that $\mu $ would be different for different colors i.e red , violet, green and so on. But if asked in the question about "lens" then won't we consider a single spectrum only?

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    $\begingroup$ chromatic aberration: en.wikipedia.org/wiki/Chromatic_aberration $\endgroup$
    – hyportnex
    Commented Feb 6, 2017 at 15:35
  • $\begingroup$ It takes a reasonable amount of effort to make a good achromatic lens. For simple optics exercises it usually doesn't matter. For real work it can matter a lot. $\endgroup$
    – Jon Custer
    Commented Feb 6, 2017 at 15:39

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The reason why the focal length of a lens depends on the wavelength is the same as the reason why a glass prism can separate the wavelength of light into a rainbow: the refractive index ($\mu$ in your question, I presume) depends on the wavelength of the light. This is called dispersion.

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According to lens maker's formula, f ∝1/μ and since μ ∝1/λ, thus in a way, f ∝ λ.

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