Proof of the Laws of Reflection

Introduction 

Reflection:

The change in direction of a wavefront at an interface between two distinct media such that the wavefront returns to the medium from which it originated is known as reflection.

The law of reflection says that for specular reflection the angle of incidence is equal to the angle of reflection. Mirrors are the ideal illustration of specular reflection.

Laws of Reflection:

The laws of reflection are as follows:

1. At the point of incidence, the incident ray, the reflected ray, and the normal to the reflecting surface are all in the same plane.
2. The incident ray’s angle with the normal is the same as the reflected ray’s angle with the same normal.

Both laws can be derived using the Fresnel equations.

The Fresnel equations (or Fresnel coefficients) describe how light (or electromagnetic radiation in general) is reflected and transmitted when it strikes an interface between two optical mediums.

Body

Proof of Laws of reflection using Huygens principle

In 1678, Huygens proposed that each point that is moved by an iridescent unsettling influence turns into a source point of a circular wave, which thus becomes auxiliary waves. These auxiliary waves decide the type of the wave at any resulting time. He supposed that the optional waves voyaged uniquely in the “forward” course, and it was never clear why they did so. There were a few blunders in the hypothesis, which were subsequently clarified by David A. B. Mill operator in 1991. The goal is that the source is a dipole (not the monopole expected by Huygens), which drops the reflected way.

In 1818, Fresnel showed that Huygens’ standard, alongside his guideline of obstruction, can clarify both the rectilinear proliferation of light and diffraction impacts. He incorporated extra self-assertive presumptions about the stage and abundance of the optional waves, and an obliquity variable to get the ideal arrangement. These presumptions have no undeniable actual establishment except for prompted forecasts that concurred with numerous exploratory perceptions, including the Poisson spot.

Poisson utilised Fresnel’s hypothesis to anticipate that a brilliant spot should show up in the focal point of the shadow of a little plate, and he derived from this, that the hypothesis was mistaken. In any case, Arago- an individual from a similar French advisory group, carried out the trial and showed that the assumption was correct. This was one of the examinations that prompted the triumph of the wave hypothesis of light over the overwhelming corpuscular hypothesis.

Types of Reflections

Reflection can be classified into 3 parts: diffuse, specular, and glossy.

Diffuse Reflection: Diffuse surfaces reflect light in many different angles. Because most things are opaque and reflect light diffusely, diffuse reflection accounts for more colour than any other sort of distribution.

Specular or Regular Reflection: Specular surfaces reflect light at the same angle as at which the light strikes the surface. Specular reflection gives objects a mirror-like appearance.

Glossy Reflection: Glossy surfaces are regular surfaces with micro surfaces at angles to the surface plane. These micro surfaces reflect the light not only specularly but also diffusely (at angles very close to the specular transmission), giving the surface a glossy appearance.

Generalised Huygens’ Principle:

The generalised principle is defined by Feynman as follows:

“In the case of optics, Huygens’ principle is incorrect. Kirchoff’s (sic) modification replaces it, requiring knowledge of both the amplitude and its derivative on the surrounding surface. This is due to the fact that in optics, the wave equation is second order in time. Because quantum mechanics’ wave equation is first order in time, Huygens’ principle is accurate for matter waves, with action replacing time.”

This shows that the generalised principle, in this case, represents quantum physics’ linearity and the fact that the quantum mechanics equations are first order in time.

Modern Physics interpretation

Not all scientists think that Huygens’ principle accurately represents reality at the microscopic level.

This can be easily seen in the following facts:

• The microscopic physics of photon generation and emission, in general, is fundamentally electron acceleration.
• Huygens’ original analysis included amplitudes only. It does not take into consideration interference because it does not contain phases or waves propagating at various speeds (due to diffraction within a continuous medium).
• Huygens’ analysis also ignores light polarisation, which suggests the presence of a vector potential.
• In Huygens’ principle, it is never explained why we choose only the forward-going versus the backward-propagating advanced wave (backward envelope).
• There is a concept of non-local behaviour in the Fresnel approximation due to the sum of spherical waves with various phases that come from separate positions of the wavefront.

Hence, on a theoretical level, Huygens’ principle is a subject of debate.

Conclusion

  The change in direction of a wavefront at an interface between two distinct media such that the wavefront returns to the medium from which it originated is known as reflection. The laws of reflection are as follows:

1. At the point of incidence, the incident ray, the reflected ray, and the normal to the reflecting surface are all in the same plane.
2. The incident ray’s angle with the normal is the same as the reflected ray’s angle with the same normal.

These laws can be proved by Huygen’s principle of wavefront. A wavefront is an imaginary surface that represents corresponding points of a wave that vibrate simultaneously.