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 white light transmitted.
If the film is of varying thickness. there will be ditlerent colors corresponding to the values of X which satisfy the above equation for different values of c, 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 c is varying. The colored effects 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 sec 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 flame), colored rings, separated by dark ones, may be seen by looking through the film at the source. the eye being focused for an infinite distance. These same rings may be seen to 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 Lippmann's method of color photography (q.v.) depend upon this principle of thin plates. The colors of the opal are (Inc to similar causes. If a soap-bubble conld be imagined crushed and crumpled up, the colors would be 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 opening: and the other is when waves with a plane wa•e-front fall upon a series of rectangular openings regularly or irregularly spaced.
(1) Diffraction Through a Rectangular Op nine. —If homogeneous waves with a plane wave-front fall upon such an opening of width b 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 hand of light fading away into two dark lines, on the farther sides of which conic 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 ing dark band X f This is illustrated by light from a distant star passing through a reetancrular openinss If light from another star apparently near the first passes through the same opening. its diffraction pattern will be the same as for the former. but shifted slightly sidewise. If the between lines drawn from the slit to the two stars is a, the pattern will he shifted sidewise a distance equal to f and a. If this amount of shift brings the maximum bright bawl 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 dose ness of the stars—so far as their angular separa tion is concerned—is then when ftana = or since a is very small, when a = This is called the •resolving power' for a rec tangular opening of width b.
Similarly when a circular opening is used, the diffraction 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 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 0 X rsin— 2 = - • 2This determines the resolving power of a scope. The greatest value 0 can have is NO°, X and under these conditions x =7-.