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waves will have been cut off and we have complete darkness below J.
This anpdes to waves other than plane with a similar proof.
To show why we can generally neglect bending, the diameter of the first zone for orange light and at 50 cm. from the light source is 0.05 cm. For a sound wave of middle C on the piano the corresponding diameter is about 76 cm.
Studying the shadow cast by an illuminated sharp edge we find that the light encroaches on the geometrical shadow, and the shadow on the light, but not with uniform diminution on both sides. Instead, there are light and dark bands in the light. These bands are called diffraction fringes.
Figure 4
Let C be a luminous point emitting spherical waves, AZB a section of a wave, ZD an opaque obstacle with a straight edge perpendicular to the plane of the paper, RV a screen.
Now to find the illumination on RV. Let us consider the point R. W is the pole of R. We can consider the illumination at R the sum of the full half of the wave above W plus that part of the wave below W that is is not obscured by the screen. We can divide the wave into half period elements as with the plane wave. Suppose WZ contains all the effective center zones of the wave. Then from
R up we have uniform illumination. Below R there is a point S such that from X, its pole, to Z there is an even number of half period elements. There will be interference of the waves coming from X and Z and we will have a spot of minimum illumination. Between the pole of T and Z there are an odd number of half period elements and we have waves from Y and Z in phase to make a bright spot at T. Between R and U there are a succession of these maxima and minima that we call diffraction fringes.
Below U the illumination will grow gradually dimmer as explained before. The main part of the illumination below U comes from the first zone that is not cut off. As these diminish gradually the diminution of effect from U to V has no maxima or minima.
If instead of ZD we have a narrow strip AB, we get fringes in the geometrical shadow as well as in the illuminated portion. The strip must be narrow enough that the light that is bent into the shadow from A and that bent in from B will overlap and produce fringes, as at XY.
These are two types of diffraction (Continued on Page 33)
F i fte e n