Page:Elementary Text-book of Physics (Anthony, 1897).djvu/446

432 point of contact were known. With this arrangement Newton found a black spot at the point of contact, and surrounding this, when white light was used, rings of different colors. When homogeneous light was used, the rings were alternately light and dark. Let $$ae$$ (Fig. 124) be the radius of the first dark ring, and denote it by $$d,$$ and let $$r$$ represent the radius of curvature of the lens. The thickness $$bc = ef,$$ which may be denoted by $$x,$$ is $$x = \frac{d^2}{2r - x}\cdot$$ Since $$x$$ is very small in comparison with $$2r,$$ this becomes $$x = \frac{d^2}{2r}\cdot$$ This distance for the first dark ring, when the incident light is normal to the plate, is equal to half the wave length of the light experimented upon. Newton found the thickness for the first dark ring $2⁄178000$ inches, which corresponds to a wave length of about $1⁄44500$ inches, or 0.00057 mm. This method affords a means of measuring the wave lengths of light, or, if the wave lengths be known, we may determine the thickness of a film at any point.

353. Effects Produced by Narrow Apertures.—It has been seen (§ 325) that cutting off a portion of a light-wave by means of screens, thus leaving a narrow aperture for the passage of the light, prevents the interference which confines the light to straight lines, and gives rise to a luminous disturbance within the geometrical shadow. This phenomenon is called diffraction. Let us consider the aperture perpendicular to the plane of the paper, and an approaching plane wave parallel to the plane of the aperture. Let $$AB$$ (Fig. 125) represent the aperture, and $$mn$$ one position of the approaching wave. To determine the effect at any point we must consider the elementary waves proceeding from the various points of the wave front lying between $$A$$ and $$B.$$ First consider the point $$P$$ on the perpendicular to $$AB$$ at its middle point. $$AB$$ is so small that the distances from $$P$$ to each point of $$AB$$ may be regarded as equal, or