How does a line of a marching band make a turn without getting out of step and how could this be related to the bending of light through a prism?

A marching band makes a turn by employing a technique called "pivoting," where the band members on the outside of the turn take larger steps while those on the inside take smaller steps. This allows the entire line to remain in sync and maintain formation. Similarly, the bending of light through a prism can be likened to this process, as different wavelengths of light refract at varying angles when entering and exiting the prism, creating a spectrum while still following the laws of refraction. Both phenomena demonstrate how coordinated movement around a pivot point can create orderly transitions, whether in marching formations or the behavior of light.