Hello Drishti Garg The refractive index goes into the scattering vector and has an influence on the calculation of size. The viscosity, however is even more important.
You may find this post of interest: https://www.materials-talks.com/blog/2017/09/26/what-is-the-maximum-viscosity-for-dls/
To add to Ulf's excellent answer, the RI of the continuous phase (liquid) is always required in DLS. If the intensity size distribution is used, then the RI of the particle is not needed. The RI of the particle is required only if the transformation from intensity to volume distribution is required. The viscosity parameter is vital as it's used in the Stokes-Einstein equation to convert the diffusion coefficient to particle size. Particles move more slowly in thicker media and there's a direct inverse relationship for hydrodynamic size and viscosity.
See another of Ulf's posts on MaterialTalks: https://www.materials-talks.com/blog/2014/08/05/faq-how-important-are-refractive-index-absorption-for-nanoparticles/
Just to add that similar arguments apply when using the Zetasizer for electrophoresis. The calculation of zeta potential from the measured electrophoretiic mobility also scales with the inverse of the viscosity. Refractive index has the same influence as for sizing.