Newton's corpuscular theory was an elaboration of his view of reality as interactions of material points through forces. Note Albert Einstein's description of Newton's conception of physical reality: [Newton's] physical reality is characterised by concepts of space, time, the material point and force (interaction betweenmaterial points). Physical events are to be thought of as movements according to law of material points in space. Thematerial point is the only representative of reality in so far as it is subject to change. The concept of the material point is obviously due to observable bodies; one conceived of the material point on the analogy of movable bodies by omitting characteristics of extension, form, spatial locality, and all their 'inner' qualities, retaining only inertia, translation, and the additional concept of force.
The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction.
In 1678, Huygens proposed that every point to which a luminous disturbance reaches becomes a source of a spherical wave; the sum of these secondary waves determines the form of the wave at any subsequent time. He assumed that the secondary waves travelled only in the "forward" direction and it is not explained in the theory why this is the case. He was able to provide a qualitative explanation of linear and spherical wave propagation, and to derive the laws of reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation which occur when light encounters edges, apertures and screens, commonly known as diffraction effects.
In 1816, Fresnel showed that Huygens' principle, together with his own principle of interference could explain both the rectilinear propagation of light and also diffraction effects. To obtain agreement with experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, and also an obliquity factor. These assumptions have no obvious physical foundation but led to predictions which agreed with many experimental observations, including the Arago spot.
Poisson was a member of the French Academy which reviewed Fresnel's work. He used Fresnel's theory to predict that a bright spot will appear in the center of the shadow of a small disc and deduced from this that the theory was incorrect. However, Arago, another member of the committee, performed the experiment and showed that the prediction was correct. (Lisle had actually observed this fifty years earlier.) This was one of the investigations which led to the victory of the wave theory of light over the then predominant corpuscular theory.
The Huygens–Fresnel principle provides a good basis for understanding and predicting the wave propagation of light. However, this article provides an interesting discussion of the limitations of the principle and also of different scientists' views as to whether it is an accurate representation of reality or whether "Huygens' principle actually does give the right answer but for the wrong reasons".
Kirchhoff's diffraction formula provides a rigorous mathematical foundation...