Raytracing on convex spherical surface, where n1>n2

I'm reading my textbook and I'm trying to figure the ray tracing of a single point of this one case that the book doesn't cover. My question is, what does the ray tracing look like when we have a convex spherical surface, with $$n_1>n_2$$?

We know that if you have a convex spherical surface, where the index of refraction, $$n_1$$, of where our point is, is smaller than the index of refraction on the other side of the spherical surface, $$n_2$$, that is $$n_2 > n_1$$, the refracted ray moves towards the normal of the surface, and we get a real image, opposite side from the object.

This is what that case would look like:

Now, if you have a concave spherical surface, where the index of refraction $$n_1$$, of where our point is, is larger than the index of refraction on the other side of the spherical surface, $$n_2$$, that is $$n_1 > n_2$$, the refracted ray moves away from the normal of the surface, and we get a virtual image, same side as the object.

This is what that case would look like:

Now, what would happen if we had a convex spherical surface, with $$n_1 > n_2$$? My gut tells me that since the index of refraction on the left side is larger, we would have the refracted ray move away from the normal of the surface, and end up with something like the concave case described above. Am I on the right track?

We know that is that the case when a plane surface is in play. But will that hold once we're dealing with a convex spherical surface?

• Why not try using Snell's law directly, when in doubt? If what you're doing is really ray tracing, then your rules of thumb aren't really needed: Snell's law should be the core of the algorithm. – Ruslan May 16 at 14:28
• If you want to run a simulation you can use my ray tracer github.com/danieljfarrell/pvtrace – boyfarrell May 16 at 17:15