Is the refractive index of a solution of four substances the median of the four substances' refractive index? I need to determine the purity of a solution and we need to discuss about the  'theoretical' refractive index of the substance that we are supposed to have.
There is no single equation that accurately predicts the refractive index of a mixture.  This reference discusses 9 approaches to estimating the refractive index of mixtures and provides the formula for each method. The simplest method is the Arago-Biot approach.  It is reasonably reliable and is described by the following formula

$$n = n_1 \phi_1 + n_2\phi_2$$

where $n$ is the predicted refractive index of the mixture, $n_x$ is the refractive index of the $x^{th}$ component, and $\phi_x$ is the volume fraction of the $x^{th}$ component.  The volume fraction of the first component is given by

$$\phi_1 = x_1 V_1 / \Sigma~ x_i V_i$$
Here $x_i$ is the mole fraction of the $i^{th}$ component and $V_i$ is the molar volume (the molecular weight divided by the density) of the $i^{th}$ component. The more ideal the liquids, the more accurate the predictions.