Why does the angle of incidence equal the angle of reflection?

The angle of incidence equals the angle of reflection due to the law of reflection, a fundamental principle in optics.

The law of reflection states that when a ray of light hits a surface, the angle of incidence is always equal to the angle of reflection. This law is applicable to all types of waves, including light, sound, and water waves. The angle of incidence and the angle of reflection are measured relative to the perpendicular (or 'normal') at the point where the ray hits the surface.

This principle is a result of the wave nature of light. When a wavefront encounters a reflective surface, each individual point on the wavefront acts as a new source of waves (Huygens' principle). The reflected wavefront is the envelope of these secondary waves. The geometry of this situation ensures that the angles of incidence and reflection are equal.

The law of reflection is also consistent with the principle of least action, which states that light travels along the path that requires the least time. When light reflects off a surface, the quickest path is one where the angle of incidence equals the angle of reflection.

This principle is fundamental to many aspects of optics, including the operation of mirrors and the reflection of light from surfaces. It is also crucial in the design of optical instruments, such as telescopes and microscopes, where precise control of light paths is required.

In summary, the equality of the angle of incidence and the angle of reflection is a fundamental principle in optics, arising from the wave nature of light and the principle of least action. It is key to understanding how light interacts with surfaces and is crucial in the design of optical instruments.