In cornea there are two factors responsible for transparency. Your teacher is correct about the fibres. The collagen fibres are arranged parallel to each other in a manner to make sure ALL points in all meridians of the cornea focus on exactly the same point; that is to say that they all have the same FOCAL length. If that wasn't true, the clinical condition that results is known as astigmatism and requires either spectacles,
lens or surgical correction.
Light refraction is same for all points, however light scattering effect is minimal and therefore the reason for the transparency.
The other reason is that cornea is avascular. This means there are no blood vessels running within cornea. This is not true of sclera because sclera has an abundant blood supply with the circulation system running WITHIN the fibrous structure. Blood vessels are definitely not designed to transmit light neatly so their presence renders maximal light absorption and scattering, and therefore the opaqueness. The fibrous arrangement in sclera is analogous to the fibrous arrangement in the connective tissue structures throughout the human body, such as in the Skin, blood vessels etc and therefore lacks transparency.
I think I answered your question from a more medical perspective. Hopefully someone else would provide an opinion of a physicist on this matter.
