Page:Light waves and their uses.djvu/138

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120

��Light Waves and Their Uses

��From each of these sources it is spread out in circular waves. If the incident wave is plane and falls normally upon the grating, all these waves start from the separate openings in the same phase of vibration. Hence, in a plane parallel to the grating we should have, as the resultant of all these waves, a plane wave traveling in the direction of the normal to the grating. When this wave is concentrated in the focus of a lens, it produces a single bright line, which is the image of the slit and is just as though the grating were not present.

���FIG. 87

Suppose we consider another direction, say ^40 (Fig. 87). We have a spherical wave, starting from the point B, another in the same phase from the point «, etc. Now, if the direction AC is such that the distance ab from the opening a to the line through B perpendicular to AC is just one wave, then along the line BC the light from the openings B and a differ in phase by one whole wave. When ab is equal to one wave, cd will be equal to two waves; hence, along BC the light from the opening c will be one wave behind the light from a, etc. ; and if these waves are brought to a focus, they will produce a bright image of the source. Since the wave lengths are different for different colors, the direction AC in which this condition is fulfilled will be different for different colors. A grating will there-

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