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how does focal length of a lens depends on the wavelength of light passed through?according to me the focal length should not change as focal length is a physical quantity of a lens so it should not change.

For a spherical mirror the focal length remains unaffected with all three parameters; wavelength, refractive index and frequency.

The focal length of the lens varies directly with the wavelength of the light used and as wavelength is inversely related to refractive index, the focal length also varies inversely with it. This is the principal cause of the phenomena of chromatic aberration. The frequency of light has no effect on the focal length.

So, focal length in creases with wavelength but decreases with refractive index and vice versa.

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Ordinary lenses, working on the basis of refraction, have a focal length which is slightly wavelength-dependent due to the wavelength dependence of the refractive index (–> chromatic dispersion). This effect leads to chromatic aberrations of imaging systems and similar problems in other applications where an optical system is used for a wide range of optical wavelengths. Lens combinations (e.g., objectives for photographic cameras) can be designed such that chromatic aberrations are minimized. Most common is the use of achromatic doublets, i.e., lenses consisting of two different glass materials chosen such that the overall chromatic aberrations are largely canceled.

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so does the focal length of a lens increases if we use a light of greater wavelength?

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