How do objects across a flat surface appear distorted?

Question

Imagine looking at an object after a planar interface.

It can be proven that if angles are small, $y'=y\frac{n_1}{n_2}$. Steps are easy but this result confuses me and I'm not sure to have understood the meaning. I find anti intuitive that looking normal to a flat interface an object looks different just because of a different index of refraction. I'm thinking for example to a flat aquarium, if we look at the surface orthogonally, dont we see fish simply as they are and where they are?

If I must believe to calculus, the answer is not (maybe the effect is small and not so important looking a fish in aquarium or under the sea surface, otherwise natural selection supported birds hunters to take into account the optical effects to strike their prey through the body of water) but... does it looks smaller or bigger? (I mean, on the one hand it is shorter on the other hand it is closer to the surface)

Answer 1

Suppose $n_1 = n_2$. If that was true, light would not bend at the interface. It would travel straight from the object to your eye. The direction of the light would tell you where the object is.

As it is, you see light coming from a different direction. This makes the object appear as if it was in a different place. To understand this, again suppose $n_1 = n_2$, but also the object was at the end of the dashed line. You would see the same thing as the distortion you really see.