Does the index of refraction of the sun's corona and solar wind contribute to the bending of light It's not hard to imagine that the sun's corona and surrounding solar winds have an optical density that can affect the index of refraction near the surface of the sun and bend light in these regions. Is this effect appreciable? Is it included in general relativity calculations for gravitational lensing?
 A: Yes, modern observations of gravitational lensing by the sun account for refraction from the solar corona.  The strength of refractive effects depend on the frequency (or wavelength) of light.  Higher frequency (shorter wavelength) light will be less effected by refraction from the corona.
For example, I don't think Eddington and company needed to worry about coronal refraction when using visible light.  They also used instruments with relatively low measurement precision, so the refractive effects would be below their measurement uncertainty.
More modern tests of GR based on gravitational lensing by the sun use radio quasars as the distance object, not visible light emitting stars.  Lebach et al (1995) observed lensing of quasar 3C279 using very long baseline interferometry (VLBI).  The paper is paywalled but in the abstract they mention "plasma-corrected group delays" referring to how they must account for the refractive effect of the radio waves propagating through coronal plasma.
Fomalont et al (2009) achieved parts per $10^4$ level precision of the gravitational deflection, of the same quasar.  While they observed with a few different radio bands ($15$, $23$, $43$ GHz) their result was dominated by the $43$ GHz observations, which was least affected by coronal refraction due to the higher frequency (shorter wavelength).  In that paper they state that they chose not to even try with the $2.3$ and $8.4$ GHz receivers because they are "subject to severe scattering by the coronal refraction within about four degrees of the sun."
