How would we see the earth if refraction of light was significantly stronger? On worldbuilding.SE there is a question about the cosmological consequences of a world with super-high refraction and atmosphere opaqueness.
I'm assuming the easiest way to minimally change the laws of physics is to make the effective speed of light more dependent of the medium it travels through. Unless this is incredibly far from the truth, I don't wish you to discuss that in your answer in much detail.
Instead I want to focus on the following: what apparent shape would the earth and (large) objects on it have as observed from various heights relative to the surface (I'm assuming things get interesting when you get close to the surface) and what would different wavelengths of light breaking at different rates entail?
I'm inclined to believe that the world would look like one part of a two sheeted hyperboloid.
 A: Let's pick apart the problem from various vantage points to see if an answer becomes interesting:


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*Standing on the ground  Looking around, the world will not look much different in a high refractive index material.  Think about swimming in a pool.  A high index makes objects appear closer than a low index (the optical path is shorter).  Therefore, objects would appear closer, but only in comparison to a world of low refractive index.

*A satellite observing the ground  Here things start to get interesting.  Like most physics, the real fun happens at the interface between two different media.  In a geo-stationary orbit, looking down on the planet's surface, all the features would appear to be at the surface in almost a flat manner.  The high index material has no optical path compared to the physical distance.  Therefore, everything appears painted on the surface of the interface between the atmosphere and vacuum.  Even depth perception becomes difficult.  Very high features appear flat.

*Approaching the planet from a significant distance  When you approach the planet from afar and you are close enough to perceive it as a disc in space, there are two dominant effects that come to mind:  refraction and Fresnel reflection. 
A. Refraction  The refraction is extremely strong.  Therefore, looking at the atmospheric limb, it will appear as a very strong lens, bending light straight down towards the surface.  Again, the features on the surface will appear printed at the interface between the atmosphere and vacuum.  Even at grazing incidence, at the limb, light rays will refract straight down to the planet's surface.
B.  Fresnel reflectance  This is the big bummer.  The larger the index of refraction difference between two materials, the larger the impedance mismatch.  Therefore, energy (light) does not couple through the interface very well.  The surface becomes highly reflective.
$$R={{(n_1 - n_2)^2} \over {(n_1 + n_2)^2}}$$
So, the surface will appear very reflective.  It the atmosphere is very dense, then the interface between vacuum and atmosphere will transition over a short distance, enhancing this reflectivity.  If on the other hand, the transition is occurs over a large range, then the reflectivity will be much less and the surface will appear as I've described, "painted" on the shell of the atmosphere.
If you want to see this in real life, take a look at Calcite.
