LIGHT. 349 ness of the stars — so far as their angular separa- tion is concerned — is then when Jt&na = y or since a is very small, when X This is called the 'resolving power' for a rec- tangular opening of width h. Similarly when a circular opening is used, the dili'raction pattern consists of a bright spot fading rapidly into a dark ring, then a faint ring, a dark ring, etc.; and if the diameter of the opening is d its resolving power may be shown to be a = 1.22^ Similarly, if two point-sources are at a dis- tance X apart and are at such a distance from a lens that the angular aperture of the lens as seen from either point is 0. the lens cannot 'resolve' the points if x is so small that e X xsing-^- This determines the resolving power of a micro- scope. The greatest value 8 can have is 180°, and under these conditions a; =: 7;. ( If the two points are in a medium whose in- dex of refraction with reference to air is n — e.g. oil immersion microscopes — this limiting distance X •' ^ = 2^"> (2) Diffraction Through a Series of Parallel Rectanyuhir Openings Regularli/ tipaced. that is, a 'grating.' ( See Diffr.ction and Diffraction Gratings.) If the width of each opening is 6 and of each opaque strip separating the openings is a, the sum {a --b) or e is called the 'grating- space.' In general these gratings are made by ruling lines by means of a diamond point on a glass plate. Where the diamond makes scratches the surface is rendered opaque, and the spaces in between are transparent slits. An equally good ar- rangement is to rule lines on a polished metallic mirror, and use it as a reflecting grating. As a rule the grating-space is made very small, there being as many as Lj-OOO or 20.000 lines to the inch. (See DmoiXG Engine.) If homogeneous waves with a plane wave-front are incident upon a grating at such an angle that the perpendicular to the wave-front makes an angle i with the perpendicular to the grating, the waves diffracted through the openings will be broken up into beams leaving the gi'ating in such direction as to make with the perpendicular to the grating angles given by the value of Sin the formula XX z= e (sin i -f- sin 6), where N is any whole number. 0, 1, 2, 3, etc., positive or negative. The simplest case is when the incident light is perpendicular to the grating, that is i ^ ; hence NX — = sm ff. e The best method of observing these diffracted beams is to focus them upon a screen by means of a lens. Tlie diffraction pattern will be a series of bright bands corresponding to the above formula, with other faint maxima and minima LIGHT. unless the giating-space is small. If this is the case, the subsidiary maxima disajjpear and tiie bright bands shrink up into line lines, the smaller the grating-space the narrower these lines of light. Thus there will be lines of light for -> 2X e — 0,e = ehi ^' e = sin — , etc.; that is, there is a central line and others on each side of this, forming what are called the first, second, etc., spectrum according as N = 1, 2, etc. The grating-space can be measured; the order of the spectrum is known in any particular case; 8 can l)e measured by a goniometer, and so the wave- length of the ether-waves may be determined. This is one of the most accurate methods known for the measurement of the wave-lengths of ether-waves. If white light is used, each component train of waves will have its own maxima at definite angles ; and .so the light is analyzed into its parts, forming a central white image and series of colored spectra on each side. It may be shown that if m is the entire number of grating- spaces and if two trains of wave of wave-length X and X + AX (where AX is small) are viewed in their spectra of the Xth order, they will have bright lines so narrow as to be separate enough to recognize the existence of both if XX AX = — r=' T-r^ = niN is defined to be the 'resolv- mX AX ing power of the grating.' A spectrum in which each train of waves of a definite wave-length is represented by a 'line' of light as fine as pos- sible is called a 'pure' spectrum. When diffraction through a great luimber of equal parallel slits irregularly spaced takes place, it may be shown that the effect is simply that of a single slit, only greatly intensified. Simi- larly, if a great number of circular openings of the same size or of circular disks of the same size are placed at random in front of a point-source of light, the diffraction pattern is simply that due either to a single opening or to a single disk. The color halos around the moon are in certain cases due to the ditfractioii past circular disks of floating drops of water. PoL.RiZATiON. All the phenomena so far dis- cussed depend for their explanation upon the assumption that light is due to wave-motion : and therefore similar ones may be observed with all kinds of wave-motion: for instance, aerial waves may be reflected, refracted, and ilifTracted. and may be made to interfere. But there are certain other phenomena in the case of light which establish the fact that the ether-waves which produce light are transverse, that is. the vibra- tion in the ether is at right angles to the direc- tion of advance of the waves. In other words, the vibration in the ether is in the wave-front as the waves advance in the pure ether or through isotropic material bodies. This may l)e proved in several ways. Perhaps the simplest is this: cut two identical plates of a crystal of tourmaline: let ordinary while light from the sun or from a lamp pass through one of these plates and then let it fall perpendicularly upon the other: if this second plate is turned slowly around an axis parallel to the rays of liaht, it will be noticed that, during one complete revo- lution of the plate through .StlO". there are two positions differing by 180° for which no light emerges from the second plate, while half way
