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Question
Will the focal length of a lens for red light be more, same or less than that for blue light?
Solution
The refractive index depends on colour of light or wavelength of light.
Cauchy's equation: `mu = A+ B/lambda^2 + C/lambda^4 + ...`
As λred > λblue hence μred < μblue
Hence parallel beams of light incident on alens will be bent more towards the axis for blue light compared to red.
By lens maker's formula,
`1/f = (mu - 1)(1/R_1 - 1/R_2)`
The refractive index for red light is less than that for blue light μred < μblue
Hence `1/f_("red") < 1/f_("blue") ⇒ f_("red") > f_("blue")`
Thus, the focal length for red light will be greater than that for blue light.
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