Is it because its internal structure is Crystalline? I mean by transparency following.
No, the Cornea is mostly fibrous - not crystalline.
As for the physics of optical transparency - here's an elementary introduction
In order to go through a material evenly, light has to avoid two things:
being scattered off into another direction.
- Why glass is transparent?
- Why is air invisible?
- How can a body be transparent?
- Why is the atmosphere transparent in the visible spectrum?
- Why does paper become translucent when smeared with oil but not (so much) with water?
- Why do wet objects become darker?
- Transparency of materials
- Why isn't light scattered through transparency?