Suppose refractive index $\mathrm{\mu }$ is given as $\mathrm{\mu }=\mathrm{A}+\mathrm{B}/{\mathrm{\lambda }}^2$ ? where A and B are constants and $\mathrm{\lambda }$ is wavelength, then the dimension of B is same as that of:

$\mathrm{As}, \mathrm{\mu }=\frac{\mathrm{Velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{vacuum}}{\mathrm{Velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{medium}}$
The refractive index $\mathrm{\mu }$ is dimensionless, so each term on right hand side is dimensionless. Hence, $\frac{\mathrm{B}}{{\mathrm{\lambda }}^2}$ is also dimensionless. This implies that dimensions of B will have the dimensions of ${\mathrm{\lambda }}^2$, i.e., of area.