The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicistAugustin-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 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 that 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 that 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 that 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 for diffraction, based on the wave equation. The arbitrary assumptions made by Fresnel to arrive at the Huygens–Fresnel equation emerge automatically from the mathematics in this derivation. 

A simple example of the operation of the principle can be seen when two rooms are connected by an open doorway and a sound is produced in a remote corner of one of them. A person in the other room will hear the sound as if it originated at the doorway. As far as the second room is concerned, the vibrating air in the doorway is the source of the sound.