Explain briefly why the intensity reflected off the back surface of the film (i. e., the right surface, where there is a liquid-to-air interface) is 2.78% of the intensity of the beam that was transmitted through the front surface.

Explanation:

Taking the incident light to be traveling in the + x-direction so that it is at normal incidence to the left side of the film(referred to as the "Front side"). This means the beam transmitted into the liquid is essentially as strong as the incident beam.

Almost all the light that is reflected off the back surface will get through the front surface. (But only 2.78% gets re-reflected off the the front surface back to the right) this means that there are two beams reflected to the - x-direction, one from the front surface and one from the back, and these beams are of almost equal intensity.

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true tan speed = ang vel x radius