Page:Elementary Text-book of Physics (Anthony, 1897).djvu/447

§353] the time of passage of the light from each point of $$AB$$ to $$P$$ may be made the same, by placing a converging lens of proper focus between $$AB$$ and $$P.$$ Then all the elementary waves from points of $$AB$$ meet at $$P$$ in the same phase, and the point $$P$$ is illuminated. Now consider a second point, $$P',$$ in an oblique direction from $$C$$ (Fig. 126), and suppose the obliquity such that the time of passage from $$B$$ to $$P'$$ is half a vibration period less than the time of passage from $$C$$ to $$P',$$ and a whole vibration period less than the time of passage from $$A$$ to $$P'.$$ Plainly the elementary waves from $$B$$ and $$C$$ will meet at $$P'$$ in opposite phases, and every wave from a point between $$B$$ and $$C$$ will meet at $$P'$$ a wave in the opposite phase from some point between $$C$$ and $$A.$$ The point $$P'$$ is, therefore, not illuminated. Suppose another point, $$P$$ (Fig. 127), still further from $$P,$$ such that $$AB$$ may be divided into three equal parts, each of which is half a wave length nearer $$P$$ than the adjacent part. It is plain that the two parts $$Bc$$ and $$ca$$ will annul each other's effects at $$P'',$$ but that the odd part Aa will furnish light. At a greater obliquity, $$AB$$ may be divided into four parts, the distances of which from the point, taken in succession, differ by half a wave length. There being an even number of these parts, the sum of their effects at the point will be zero. Now let us suppose the point $$P$$ to occupy successively all positions to the right or left of the normal. While the line joining $$P$$ with the middle of the aperture is only slightly oblique, the elementary waves meet at $$P$$ in nearly the same phase, and the loss of light is small. As $$P$$ approaches $$P'$$ (Fig. 126), more and more of the waves meet in opposite phases, the light grows rapidly less, and at $$P'$$ becomes zero. Going beyond $$P'$$ the two parts that annul each other's effects no longer occupy the whole space $$AB,$$ some of the points of the aperture send to $$P$$ waves