(If the two points are in a medium whose in dex of refraction with reference to air is it—e.g. oil immersion mieroseopes—this limiting distance X is x = (2) Diffraction Through a Series of Parallel Rectangular Openings Regularly Spaced, that is, a 'grating.' (See DIFFRACTION AND DIFFRACTION URATINGS.) If the width of each opening is b 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 15.000 or 20.000 lines to the inch. (See DIVIDING 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 perpendieular to the grating. the waves diffracted through the openings will be broken up into beams leaving the grating in such direction as to make with the perpendicular to the grating angles given by the value of Bin the formula NX=e (sin i 0), where 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 = 0; hence NX —sin 0.
The hest method of observing these diffracted herons is to focus them upon a screen by means of a lens. The diffraction pattern will he a series of bright hands corresponding to the above formula, with other faint maxima and minima unless the grating-space is small. If this is the ease, the subsidiary maxima disappear and toe bright bands shrink tip into tine lines, the smaller the grating-spa•e the narrower these hues of light. Thus there will be lines of light for
x 1 2X 0= 0,0= sin 0 sin c , etc.; that is, there is a central line and others on each side of this, forming what are called the first. seeond, etc., spectrum according a. N = I, 2, etc. The grating-space can be measured; the order of the spectrum is known in any particular case; 0 can be measured by a guniometer, 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 tic is the entire number of grating spaces and if two trains of wave of wave-length X and X + AX (where AA is small) are viewed in their spectra of the Nth order, they will have bright lines so narrow as to be separate enough to recognize the existence of both if X X AX mN - • = niN is defined to be the •resolv mg 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 tine as pos sible is called a 'pure' spectrum.
When diffraction through a great number 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 eircular 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 eases clue to the diffraction past circular disks of floating drops of water.