In this problem, light is incident on a beamsplitter, and then it travels around loops of optical fibre before eventually coming out the other end. I needed to find the intensities of E1 and E2. (Attached image)

This is what I did:

Let

be the reflected light from E_{in} and let

be the transmitted light. Also let "delta" be the phase the light travels through in the loops of optical fibre.

Then

And

But the Question says that "you should find all light reflected back to the output", meaning E2=0!

What have I done wrong? Thanks