THE DIFFRACTION GRATING.
The case of parallel rays of light falling on a series of equally-spaced long and narrow rectangular apertures may be now considered. This arrangement of apertures is termed a grating. By the wave theory it can be proved that the light which enters slit s (Fig. 771) takes the same time to get to the grating along any of the paths through the lens L,. Since the light is entirely from one small odd number of half wave-lengths behind that corning from b, there will be no re sultant light at z from these two aper tures, and therefore no image. As the same thing happens with each pair of apertures, no image at all will be formed in this direction. If the difference of path be an even number of half wave-lengths source, it will all be in the same phase of vibration at the time it reaches the grating. This idea is usually expressed by saying that the wave front is parallel to the surface of the grating. Since the light is of small wave-length, as it passes through the slits it diffracts practically in all directions from each slit. In the dia gram, therefore, for the sake of sim plicity, but one colour has been considered, and only one direction for that colour. On interposing the lens L, at right angles to these parallel rays, a real image of the slit will be obtained at z under certain conditions. The lens is now parallel to the line K b,. Consider the light passing
through a to a,. The light at point b is ultimately added to that at to make the image at the principal focus of But these two beams are not obliged to arrive at the image in the same phase. Between these two corresponding rays there is a difference of path equal to the difference of a b arid a, This at once enables the difference of phase to be esti mated. If the beam going from b, is an there will be a maximum of light, and consequently there will be a bright image at the focus of Directly opposite to the original direction of the incident light at al a bright image would be made by L, when L, is placed in the proper position for focussing it, since all the light arriving at the focus would be in the same phase, having traversed equivalent paths. It would seem, at first sight, that on moving towards z the light should gradually fade from the place opposite the middle of the grating, to a line of darkness, and then rise to a maximum of light to fade away again, repeating these effects as far as observations were taken in the direc tion 3r z. But, owing to the interactions of the light from all the apertures, periods of darkness broken by distinct lines of light are seen when the light falling on slit s is monochromatic.