Assertion A is correct. When light waves travel through different media with different indices of refraction, the speed of light changes, which in turn changes the phase of the light waves. This is because the phase of a wave is directly related to the distance it has traveled, which in this case is affected by the speed of light in the different media.

Reason R is also correct. The speed of light in a medium is determined by its refractive index. When light enters a medium with a different refractive index, its speed, and therefore its wavelength, changes. This is described by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in a vacuum, and n is the refractive index of the medium.

Moreover, R is indeed the correct explanation of A. The change in wavelength (and therefore phase) of the light waves in different media (as explained in R) is the reason why the phase difference changes when light waves travel through different media with the same thickness but different indices of refraction (as stated in A).