diffraction grating, the features generally become sharper. The fourth figure, for example, shows a comparison of a double-slit pattern with a pattern formed by five slits, both sets of slits having the same spacing between the center of one slit and the next. Approximations The problem of calculating what a diffracted wave looks like, is the problem of determining the phase of each of the simple sources on the incoming wave front. It is mathematically easier to consider the case of far-field or Fraunhofer diffraction, where the point of observation is far from that of the diffracting obstruction, and as a result, involves less complex mathematics than the more general case of near-field or Fresnel diffraction. To make this statement more quantitative, consider a diffracting object at the origin that has a size . For definiteness let us say we are diffracting light and we are interested in what the intensity looks like on a screen a distance away from the object. At some point on the screen the path length to one side of the object is given by the Pythagorean theorem If we now consider the situation where , the path length becomes This is the Fresnel approximation. To further simplify things: If the diffracting object is much smaller than the distance , the last term will contribute much less than a wavelength to the path length, and will then not change the phase appreciably. That is . The result is the Fraunhofer approximation, which is only valid very far away from the object Depending on the size of the diffraction object, the distance to the object and the wavelength of the wave, the Fresnel approximation, the Fraunhofer approximation or neither approximation may be valid. As the distance between the measured point of diffraction and the obstruction point increases, the diffraction patterns or results predicted converge towards those of Fraunhofer diffraction, which is more often observed in nature due to the extremely small wavelength of visible light. Multiple narrow slits A simple quantitative description Multiple-slit arrangements can be mathematically considered as multiple simple wave sources, if the slits are narrow enough. For light, a slit is an opening that is infinitely extended in one dimension, and this has the effect of reducing a wave problem in 3D-space to a simpler problem in 2D-space. The simplest case is that of two narrow slits, spaced a distance apart. To determine