INTERFERENCE — FRESNEL'S MIRROR EXPERIMENT. 



169 



while the observed effects are consequences absolutely necessary of the undu- 

 latory theory. 



Two mirrors, AB and AC, meet at a very 

 obtuse angle at A. II is a minute radiant 

 point. The best radiant for this purpose is 

 the concentrated light from a small solar beam 

 introduced into a dark room and brought to a 

 focus by a lens of small focal distance. Rays 

 of liglit from It, reflected by the mirrors, pro- 

 M ceed as from the points S and S', which are 

 in the perpendiculars let fall from 11 on the 

 planes of the mirrors severally, and as far 

 behind them as II itself is before. If the mir- 

 rors AB and AC were in one and the same 

 plane, the points S and S' would coincide, or 

 there would be but one image of R formed by 

 the reflection; and the two images will be 

 licarer to each other, just in proportion as the 

 angle CAB approaches to two right angles. 

 The spherical waves proceeding from R as a 

 centre would be reflected from a single mirror in a system entirely similar to the 

 original one, proceeding apparently from the image behind the mirror. When 

 there are two mirrors and two such images, there will be two such systems of 

 spherical wr..ves, which will intersect each other in arcs more and more nearly 

 coincident, as the images which are their centres are nearer together. In the 

 figure there are drawn, with equal radii, from S and S', a succession of equidis- 

 tant circular arcs, which may be considered to represent the crests of the suc- 

 cessive waves. The intermediate dotted arcs may be taken for the hollows. 

 According to the principles already laid down there should be increased energy 

 of movement — that is an increase of brightness — wherever two ridges or two 

 hollows cross each other ; and diminished movement, or a diminution of light 

 where a hollow crosses a ridge. And as it is obvious, on inspection, that the 

 intersections Avill be more widely separated from each other in proportion as the 

 centres are nearer to each other, it follows that these theoretically predicted 

 effects Avill be more conspicuous and more decided in proportion as the planes of 

 the two mirrors approach coincidence. If the light reflected from such a pair 

 of mirrors be received upon a screen, it Avill be obvious that, whatever be the 

 distance from S and S', there will be a point, as a, where the radii Sa and S'a 

 will be equal ; and as this will be true of all points iu a line through a })arallel 

 to the intersection of the planes of the mirrors, there should here be a coincidence 

 of movements, and accordingly a bright stripe. At a little distance on each 

 side of this stripe there will be found parallel lines, in which the radius from 

 one of the centres will exceed that from the other by the length of one entire 

 undulation; and in these lines the movements will be once more in coincidence, 

 and the light will again be in excess. But between them and the central line 

 there will be found other positions in which the radii will difter by only half an 

 undulation ; and, as the movements in these positions will be directly opposed 

 to each other, the light should disappear. Extending this reasoning, we should 

 look for a series of stripes alternately dark and bright on each side of the cen- 

 tral bright stripe, at distances sensibly equal to each other. These conclusions 

 arc fully confirmed by experiment.* 



* Prof. Potter, of London, affirms, in opposition to all other experimenters, that the central 

 stripe in this experiment is often seen dark instead of light ; and in fact more usually so 

 than otherwise. — \_Londo7i Journal of Science, XVI, 1840. Also, Plnjsical Optics, I^oudon, 

 1850.] Prof. Baden Powell, on the other hand, states that he has endeavored to verify this 

 assertion with every possible attention to the conditions prescribed by Prof. Potter, but 

 entirely without success. — [^A General and Elementary Vicic of the Undulutunj Theory, Sfc, 

 Loudon, 184L1 



