. The Bell System technical journal. Telecommunication; Electric engineering; Communication; Electronics; Science; Technology. CLASSICAL THEORY OF LIGHT 737 To prove this, and to find the magnitude of these equal steps, one may proceed as follows. Omitting the lens again, consider in the grating any two consecutive slits k and {k + 1), and on the very. Fig. 2. distant screen two field-points P and P' separated by the same distance c as separates corresponding points of the two slits—that is, the period of the grating. Write down successively the formulae for the vibrations produced by ^ at P a
. The Bell System technical journal. Telecommunication; Electric engineering; Communication; Electronics; Science; Technology. CLASSICAL THEORY OF LIGHT 737 To prove this, and to find the magnitude of these equal steps, one may proceed as follows. Omitting the lens again, consider in the grating any two consecutive slits k and {k + 1), and on the very. Fig. 2. distant screen two field-points P and P' separated by the same distance c as separates corresponding points of the two slits—that is, the period of the grating. Write down successively the formulae for the vibrations produced by ^ at P and by (/^ + 1) at P'. They are, respectively: A sin (nt — niro — e^); A sin {nt — mro' — e^•+l). Since P lies in the same direction from k as P' from (k + 1), these two are equal; hence: ei+i - €i = m{ro' - Tq). (3) Here the factor {r^ — Tq) on the right is the difference between the distances from the origin to P' and to P. In the limit when these distances become infinitely great, all the lines from the origin and the slits to P and P' become parallel and inclined to the plane of the grating by the angle of which the cosine is /3; and the difference be- tween the paths to P' and to P from the origin attains the limiting value c/3. Hence in the limit: efc+i - ek = mc0. (4) This is the "step" or difference in phase between the contributions of successive slits to the vibration at the field-point. The expression looks more familiar if we put d for the angle between the normal to the. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original American Telephone and Telegraph Company. [Short Hills, N. J. , etc. , American Telephone and Telegraph Co. ]
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