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Is focal length directly proportional to wavelength or inversely proportional to wavelenth?

Lower wavelength of incident light means more deviation so smaller focal length for the lens. 

More wavelength of incident light means less deviation so larger focal length for the same lens.

So, we ca say focal length is directly proportional to the wavelength of lens.

For the mirror, focal length is independent of the wavelength of light.

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focal length is inversely proportional to wavelength.

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Hi,
The lens maker’s formula is given by,
μ is the refractive index of the lens.
This equation is valid strictly for a monochromatic light. Since, the μ of a lens varies with the change in wavelength of incident light as:
(A, B, C are constants)
Thus, refractive index is inversely proportional to the square of the wavelength of the incident light. Focal length of a lens is inversely proportional to the refractive index of the lens. So, the focal length is directly proportional to the square of the wavelength of the incident light. Since, wavelength of violet light is smaller than red light; focal length for violet light will be smaller compared to the focal length of the red light.

 
  • 1
Hi,
The lens maker’s formula is given by,
μ is the refractive index of the lens.
This equation is valid strictly for a monochromatic light. Since, the μ of a lens varies with the change in wavelength of incident light as:
(A, B, C are constants)
Thus, refractive index is inversely proportional to the square of the wavelength of the incident light. Focal length of a lens is inversely proportional to the refractive index of the lens. So, the focal length is directly proportional to the square of the wavelength of the incident light. Since, wavelength of violet light is smaller than red light; focal length for violet light will be smaller compared to the focal length of the red light.

 
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