Optics: Spherical Interface -- Real and Virtual Images

1. The problem statement, all variables and given/known data



If you have a spherical interface between two different "media" (like air and water), and an object is placed in the one with the lower index of refraction, with the interface being convex toward the object, how can you tell if the image will be real or virtual?



Here's a picture of the two different possibilities. The white area has a lower index of refraction than the blue area, so the rays will bend toward the normal when they strike it. But how far they bend determines if the image will be real or virtual. I know about Snell's Law, but I think it would be difficult to apply here since the interface is not flat. Also, I am pretty sure whether the image is real or virtual depends on the distance the object is from the interface, but I don't know how to find that distance.









2. Relevant equations



I'm sure there is a simple one somewhere but I can't find it in my notes or book :(





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Thanks!