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I was reading "Geometrical Optics Reflected Fields" chapter from "Introduction to Uniform Geometrical Theory of Diffraction" textbook.

The author assumed that the surface is perfectly conducting and therefore he only considered the reflected waves. He derived a formula for the reflected field, its polarization and the radii of curvature of its wavefront.

I have two questions:

1) If the incident wave front is spherical, the radii of curvature of the reflected waves will depend on the incident wave and the reflecting surface, but will the reflected wave front still be considered spherical?

2) If the surface is not perfectly conducting, then a transmitted electric field exists. We can use fresnel coefficients to calculate its magnitude but how can we calculate its polarization and the radii of curvature of its wavefront?