Abstract:


When the mirror rotates within the incident plane, the angle change of the reflected light is twice the mirror's rotation angle. However, when the mirror rotates out of the plane, the angle change of the reflected light is difficult to describe quantitatively. This paper combines the law of light reflection and the geometry to study the angle change of the reflected light when the mirror rotates freely in three-dimensional space. A general expression is obtained, which is related to the incident angle, the in-plane rotation angle, and the out-of-plane rotation angle. The results show that when there is no rotation within the incident plane, the angle change of the reflected light varies most rapidly with changes in the out-of-plane rotation angle. As the in-plane rotation angle increases, the angular change of the reflected light with the out-of-plane rotation angle gradually decreases until it reaches zero. These findings enhance the understanding of the behavior of reflected light when the mirror rotates in free space and provide theoretical support for light propagation in fast reflectors, scanning systems, and digital micromirror devices.

Key words: law of reflection, specular reflection, free-space rotation, fast-steering mirror, digital micromirror devices