Page:Elementary Text-book of Physics (Anthony, 1897).djvu/448

434 that are not neutralized, and the light reappears, giving a second maximum, much less than the first in intensity. Beyond this the light diminishes rapidly in intensity until a point is reached where the paths differing by half a waye length divide $$AB$$ into four parts, when the light is again zero. Theoretically, maximum and minimum values alternate in this way, to an indefinite distance, but the successive maxima decrease so rapidly that, in reality, only a few bands can be seen.

354. Effect of a Narrow Screen in the Path of the Light.—It can be shown that the effect of a narrow screen is the complement of that of a narrow aperture; that is, where a narrow aperture gives light, a screen produces darkness. Let $$mn$$ (Fig. 128) be a plane wave and $$AB$$ a surface on which the light falls. If no obstacle intervene, the surface $$AB$$ will be equally illuminated. The illumination at any point $$C$$ is the sum of the effects of all parts of the wave $$mn.$$ Let the effects due to the part of the wave $$op$$ be represented by $$I$$ and that due to all the rest of the wave by $$I'.$$ Then the illumination at $$C$$ is $$I + I',$$ equal to the general illumination on the surface. Let us now suppose $$mn$$ to be a screen and $$po$$ a narrow aperture in it. If the illumination at $$C$$ remain unchanged, it must be that the parts $$mo$$ and $$pn$$ of the wave had no effect, and if, for the screen with the narrow aperture, we substitute a narrow screen at $$op,$$ there will be darkness at $$C.$$ If, however, a dark band fall at $$C,$$ when $$op$$ is an aperture, a screen at $$op$$ will not cut off the light from $$C.$$ That is, if be illuminated when $$op$$ is an aperture, it will be in darkness when $$op$$ is a screen; and if it be in darkness when $$op$$ is an aperture, it will be illuminated when $$op$$ is a screen.

355. Diffraction Gratings.—Let $$AB$$ (Fig. 139) be a screen having several narrow rectangular apertures parallel and equidistant. Such a screen is called a grating. Let the approaching waves, moving in the direction of the arrow, be plane and parallel to $$AB,$$ and let the points $$a, c,$$ etc., be the centres of the apertures. Draw