A hollow sphere with a thickness

I wanted to create a hollow glass sphere with a thickness, like these in the picture below:

I created a sphere, use solidify. At first, it sort of looked like what I wanted, but on close inspection (alt+b to cut the sphere), it just seems to be two spheres.

How can I get a hollow sphere with a thickness?

That’s how it is supposed to work.
A better way to think of faces in such cases is that a face indicates a boundary between two materials. The faces’ normals point towards the material that has a lower index of refraction (IOR). In your glass spheres, there are two boundaries, one being the outside surface of the glass (normals pointing outwards), and the other being the internal surface of the glass (normals pointing inwards).
With a setup like this, ray tracing works as it should, as the rays should only interact when they hit a face and refract or reflect*.
See this image from Wikipedia to illustrate that:

*Ignoring volumetrics and subsurface scattering in this example.

Have you set “Fill Rim” in the solidfier modifier? That should do it.