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Is it because its internal structure is Crystalline? I mean by transparency following.

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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:

  1. being absorbed

  2. being scattered off into another direction.

See also

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  • $\begingroup$ I found out inspiring teaching on transparency of glass and why it is transparent for some frequencies( light). -youtube.com/watch?v=Omr0JNyDBI0 $\endgroup$ – alvoutila Oct 17 '12 at 17:15

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