Why is Fresnel Biprism a "Bi-" prism? Why is the Fresnel Biprism made of two separate prisms joined together at their bases? Why not use a monoprism, a single prism having the same overall geometric and optical properties as that of the combination as shown in the following diagram?

I think using a single piece of material (monoprism) instead of combining two separate pieces (biprism) will lead to less error while conducting experiments, and better results due to the following reasons:


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*In a biprism, errors can occur when the two halves are not joined properly.

*While moving a biprism during experiments, the two halves might actually slip from the intended positions.

*A biprism is not homogeneous thoroughout unlike a monoprism. The interface between the two prisms does not allow light to pass through perfectly. 
 A: Cementing two right angle prisms is much easier and less expensive than fabricating the monolithic piece.  
It's not entirely clear that a single piece would behave better than two pieces cemented.  Think of the manufacturing process.  In the single piece, the two sloping surfaces have to be ground and polished in separate operations, and the part will probably have to be moved between those two steps.  How do you maintain the alignment between slopes?  It might be possible to grind the two slopes without unblocking the prism, but the fixtures needed to do that would increase the cost even more.
Optical adhesives are pretty good.   They are very nearly index-matched to the substrates, and the thickness of the adhesive layer is very small.  The two prisms will not slip from each other.  Of all of your concerns, the cementing is certainly the least concerning.
If you think you need precision of alignment of the faces, first make sure that you really do.   Do an analysis that determines what tolerance you can tolerate :-).   Then check sources of prisms to see if their standard product meets your spec.   If they don't, then contact one of the many companies that make custom optics (I work for one) and discuss your application and needs with them.   If together you decide that in your case fabricating from a single piece offers advantages (unlikely, but it's possible) they can do it for you.  But you will pay!
