A converging lens has focal lengths f_v and f_r for violet and red...

By Cauchy's formula, the refractive index of a material depends on the wavelength of light as $\mu = A + \dfrac{B}{\lambda^2}$.

Since the wavelength of violet light is less than that of red light ($\lambda_v < \lambda_r$), the refractive index of the lens material is greater for violet light than for red light ($\mu_v > \mu_r$).

From the Lens Maker's formula, \dfrac{1}{f} = (\mu - 1) \left(\dfrac{1}{R_1} - \dfrac{1}{R_2} \right).

Since $f \propto$\dfrac{1}{\mu - 1} and $\mu_v > \mu_r$, it follows that $f_v < f_r$.