$\mu =A+\frac{B}{\lambda }+\frac{C}{{\lambda }^2}$ is dimensionally correct the dimensions of $A,B\&C$ respectively are $(\mu ,A,B,C$ are constants where $\lambda$ is wave length and $\mu$ is refractive index)

  $\begin{array}{l}given \mu =A+\frac{B}{\lambda }+\frac{C}{{\lambda }^2}\\ \text{}Refractive index \mu =\frac{\sin i}{\sin r}=M^0{L}^0{T}^0; \\ \lambda is wave length =L\\ According to principle of homogeneity\\ \text{}dimensions of A=\mu =no dimensions\\ \text{}\frac{B}{\lambda }=\mu \\ \Rightarrow B=\mu \lambda \\ \Rightarrow B=L\\ \\ \frac{C}{{\lambda }^2}=\mu \\ \Rightarrow C=\mu {\lambda }^2 \\ \Rightarrow C=L^2\end{array}$