In geometrical optics, a wave front (or crest of the wave) is defined as the locus of points having the same phase of vibration. All the points on a have the same phase, since all the molecules on this particular wave front are at their maximum displacement above the normal level. Likewise t is a wave front on which all particle are at their maximum displacements below the normal level. Half way between t and b is another wave front where the particles are (momentarily) at the normal level, but moving upward. This technical use of the word "front" is not unfimiliar; in meteorology a cold front is said to connect cities X,Y,Z, which are simultaneously experiencing a sudden drop in temperature. As the wave spreads out, the wave fronts advance, and in the case of the water wave, the radius of each circular wave front continously increases. Huygens' principle tells us how to predict a new wave front when we know the position of an earlier one. The contruction is as follows: Let every point on the wave front be considered the source of small wavelet which spreads out in the forward direction. The new wave front is the envelope of all the wavelets; that is, the line or surface tangent to all the little wavelets. If we now consider light waves spreading out in three dimensions, it is evident that the wavelets are small hemispheres, provided the speed of light is the same in all directions; hence we see that a spherical wave front will remain spherical and that the energy of the wave is carried away equally in all directions. Such directions of energy flow are called rays.
Unless specifically stated otherwise, we shall always assume that light travels through a medium equally fast in all directions; such a medium is called an isotropic medium.
Glass, water, air, Lucite, and most other common substances are isotropic, but certain transparent crystals have enough structure to give rise to "easy" and "hard" directions for the propagation of light. Such a crystal is said to be anisotropic. In an isotropic medium, the wavelets are spherical, and the rays are always perpendicular to the wave fronts. In an anisotropic medium the wave fronts are ellipsoidal.
Huygens' principle describes the propagation of light in a straight line, since wavelets from a plane wave give rise to a new place wave front, and the corresponding rays are parallel to each other. Such a plane wave front can be though of as a section of very large spherical wave front; for instance, sunlight strikes the earth is wave fronts of radius 93 million miles. For all practical purposes, such a wave front is "plane" and the rays are "parallel" to each other.
Newton never did accept the wave model, for he felt (quite justifiably) that if light waves existed they would naturally "bend around corners" and would not travel is straight lines through openings or around obstacles , as they are observed to do. Newton did not realize that the extreme smallness of the wavelengh of light compared with the size of the usual opening or obstacle could account for this behavior.
In conclusion, a wave front is a line or surface, in the path of a wave motion, where all the displacements at any point have the same phase. A point source leads to circular wavefronts, at large distances from the source they are straight lines. A ray is a line that shows the direction of the wave and is perpendicular to the wavefronts.