first note: when sharing blend files here in BA, please try to take out all non important objects/images etc from the blend file, just keeping the relevant things that show the problem…
second: The problem is quite common to new cycles users…
When light goes through a refractive material, it is bended and it will not follow a straight path. It will (in real world) produce what is called caustics.
In Cycles, the algorithm to make the render will follow the oposite direction of the ‘photons’, throwing a ray starting from the camera, checking if the hit point is under direct illumination (the shadow ray), and then throw other rays to get the indirect light.
The big problem with this method, is that the shadow ray will just test the light in a straight line, where through the refraction material, we already know the light is coming from another direction. And there isn’t a good way, from the point being shaded to find exactly which direction to test (and hence, fireflies).
Of course, with lots and lots of samples, the result should end up correct. But normally, we don’t have the time to let a render take 1/2 year just for perfection, and in most of the cases the refracted light just changes a little bit from the direct light (just like the light that comes through a window). That’s why most artists just fake the caustics with a simple transparent shader. This way, the shadow ray will find the light, because in between there’s only ‘transparency’!
Now, your file: you have caustics disabled, which will turn refractive objects opaque to light for secondary rays. This makes your inner eyes completly in the dark!
In this case, you don’t really need any caustics! The distance from the outer surface to the inner surface is so small that light will not bend enough to being noticed. So telling the glass material to become transparent for every shadow ray, will let the light getting into the inner surface, as if the outer surface wasn’t there, thought you still can see it from the camera.