LIGHT. 248 LIGHT. receiving screen to the one with the two slits is a; if the distance apart of the two slits is h — a small quantity compared with a; and if PS is X, also a small quantity, it is seen hy geometry that X _0,P — 0,P a~ b bx Hence NA = - ; and the distance apart of a the bright bands is therefore ^ ■ This distance, and both a and 6, can be measured ; so this experi- ment gives a means of determining X. It is found that as the colors change from red to yel- low to green to blue the wave-length of the corre- sponding waves becomes less. Jf white light is used, the central band at S is white, but the others are colored, all merging into each other. The wave-length of the yellow light from a sodium llaine is found to be 0.0000.5893 cm. Since the velocity of the waves is 3 x 10'° cm. per second, the wave-number for these 'yellow waves' is about 5 x 10". This is the number of vibrations per second of the atom of sodium. ( For other wave-lengths, see Spectroscopy.) It is thvis ])os- sible now to compare the indices of refraction of a given material — e.g. water — with the corre- sponding wave-lengths. A curve plotted with the indices of refraction as ordinates and the wave- lengths as abscissae is called the "dispersion curve' of the substance. There are many other ways of securing two identical slits as sources of light than the one here described, e.g. FresncVs bi-prism and double mirror; but for a full de- scription reference should be made to some treatise on light. One of the most interesting phenomena de- pending for their explanation upon interference is that of the color of 'thin plates' and of Xi'w- ton's 'rings,' as shown in the colors of soap-filnis, very thin films of glass, or when a convex glass lens is pressed closely against a piece of plane glass, hcn parallel" rays of light are incident upon a transparent film of uniform thickness, that portion which comes back, at the proper angle of rellection, is a mixture of waves which have sutVered reflection at the top surface of the film and those which, having entered the film. have been rclleeted at the lower surface and then have emerged directly at the top surface or emerged after a series of internal reflections. If the relative retardation of the component trains of homogeneous waves is such that they have difl"pren( phases ec|uivalfnt to a difference of an odd number of half wave-lengths, there will he complete interference: and it can be shown that all the wav<>s have been transmitted through the film, so there is no loss of energy. If, therefore, the incident light is white, tl^ose waves will be' absent from the reflected beam which satisfy the above condition ; and so it will appear colored. It is proved easily that if the thickness of the film is c, its index of refraction with reference to air /jL. and the ancle of incidence of the light or the lower surface of the film o. there will be complete interference in the reflected light for a train of waves whose wave-length in the film is X if NX = 2MCoso, where N is any whole number. It is evident that the transmitted light is in any case complementary to that reflected; but there will always be differences in the apparent brightness of the colors, because there is so much wiiite light transmitted. If the film is of varying thickness, tliurc will l)e dillerent colors corresponding to the values of
which satisfy the above equation for dillerent
values of t, the thickness. If homogeneous light — all of one color — is used, there will be seen colored bands separated by dark ones, depending upon the fact that the above equation is satisfied by different values of N (0, 1, 2, 3, etc.) for the same value of X, if e is varying, the colored ell'ects seen with white light "depend upon the superposition of these colored bands due to the components of white light. It should be noted, however, that in order to see these colored bands the eye must be focused on the surface of the film, and a comparatively large source of light must be used. This is the explanation of New- ton's rings. If the film has perfectly parallel plane faces and is illuminated by a large source of homo- geneous light (e.g. a tlame), colored rings, separated by dark ones, may be seen by looking through the film at the source, the eye being focused for an in/inite distance. These same rings may be seen t(] better advantage if a tele- scope focused for infinity is used to view the light. It is in this manner that the interferom- eters' of Michelson and of Fabry and Perot are used. The colors obtained in Lippinann's method of color photogi-aphy (q.v. ) depend upon this principle of thin plates. The colors of the opal are due to similar causes. If a soai)-l)ul)ble could be imagined crushed and crumpled up. the colors would lie like those of the opal. There are two cases of diffraction which de- serve special attention; one is when light with a plane wave-front falls upon a single rectangu- lar or circular o]ipning; and the other is when waves with a plane wave-front fall upon a series of rectangular openings regularly or irregularly spaced. ( 1 ) Diffraction Through a Rectangular Opening. — If homogeneous waves with a plane wave-front fall upon such an opening of widtli /) and are then brought to a focus on a screen by a con- verging lens, it is observed that the illumination on the screen consists of a narrow band of light fading away into two dark lines, on the farther sides of which come two faint bright lines, etc.. the central bright line being much more intense than the successive lines. This is called a 'diffraction pattern.' If f is the focal length of the lens, the distance from the centre of the central light band to the centre of the neighbor- X ing dark band is / t- This is illustrated by- light from a distant star passing through a rectangular opening. If light from another star apparently near the first passes through the same opening, its dill'raction jiattern will be the same as for the fonner. but shifted slightly sidewise. If the angle between lines drawn from the slit to the two stars is a, the pattern will be shifted sidewise a distance equal to f and a. If this amount of shift brings the maximum bright band of one pattern to coincide with the minimum of the other, the resultant diffraction pattern will be such that it is just possible to distinguish the presence of two patterns. If the pattern is shifted less, it is impossible to recog- nize the presence of the two. The limiting close-
