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We can also see that in the rough coating image, the base layer reflection is much more diffused, this is due to the scattering of rays through the top layer, which is achieved by the roughness approximation.

Rough/bumpy gold with a smooth purple coating

These images are of a similar material configuration, but with the roughness and bump map on the base layer instead of the top layer. This configuration demonstrates that even when the top layer is smooth, it still creates a difference in look due to the refraction and compression of rays that reach the base layer.