Final answer:
The composition of rotations Ro,90 o ry differs from ry o Ro,90 due to the non-commutative nature of rotation operations. In the context of Brewster's angle and light polarization, the sequence of these rotations affects the result, indicating that the operations are not interchangeable.
Step-by-step explanation:
The question asks about a mathematical composition of rotations in Physics, specifically dealing with light polarization and Brewster's angle. The composition of rotations Ro,90 o ry is not necessarily equivalent to ry o Ro,90 due to the non-commutative nature of rotation operations in three-dimensional space. This can be related to the concept of the Brewster's angle where the sum of the angle of incidence (θb) plus the angle of refraction (θ'b) should be 90 degrees, as light polarization upon reflection depends on the incident angle.
In optics, Brewster's Law can be used to demonstrate that when light is polarized at a specific angle known as Brewster's angle, the reflected and refracted rays are perpendicular to each other. If we consider Ro,90 as a rotation about the optical axis by 90 degrees and ry as a rotation about an axis in the plane of incidence, the sequence in which these rotations are applied matters. Thus, Ro,90 o ry is generally not equivalent to ry o Ro,90 because of the fundamental properties of rotation operations.