Focal length of a convex lens will be maximum | vedclass

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(C) According to the lens maker's formula,the focal length $f$ of a lens is given by:$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \ri

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red light

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(C) According to the lens maker's formula,the focal length $f$ of a lens is given by:$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$where $\mu$ is the refractive index of the lens material.From this,we can see that $\frac{1}{f} \propto (\mu - 1)$,which implies $f \propto \frac{1}{\mu - 1}$.According to Cauchy's dispersion formula,the refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ of light $(\mu \propto \frac{1}{\lambda})$.As the wavelength $\lambda$ increases,the refractive index $\mu$ decreases.Since $f \propto \frac{1}{\mu - 1}$,a decrease in $\mu$ leads to an increase in the focal length $f$.Among the given colors,red light has the maximum wavelength $(\lambda_{red} > \lambda_{yellow} > \lambda_{green} > \lambda_{blue})$.Therefore,the refractive index $\mu$ is minimum for red light,which results in the maximum focal length for red light.

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