Reflection at a Plane AB (fig. 2) to be a plane wave-front, moying in the direction Bb perpendicular to AB. Let AL be the reflecting surface, and let the intersection of the plane of the wave-front with the surface be a line through A perpendicular to the paper. When B has arrived at b, A would bare arrived at 13, and P at q (where bfi is parallel to BA, and Pq and A/3 to Bb), had it not been for the reflecting surface. Hence, when B is at b, A has diverged into a sphere of radius A/i, P from p into a sphere of radius and so for each point of the wave-front. Now, the spheres so about A and p as centers obviously touch the plane bfi; conse quently they touch the other plane ba, which makes the angle Aba equal to Ab/3. Now, b7ra is the front of the reflected wave. and Aa is the direction in which it is proceeding. Hence, obviously, the ordinary laws of reflec tion. See CATOPTRICS.
lb:fraction at a Plane Surface into an Isotropic Medium.—Here we take account of the change of velocity which light suffers in passing from one medium to another. In fig. 3, A, P, B, b, p, g, and /3 represent the same as before —but suppose Aa now to represent the space through which the wave travels in the second medium, while it would travel from B to b in the first. With center A, and radius Aa, describe a sphere. Let ba touch this sphere in a. Then ba is the front of the refracted wave. For, if pn be drawn perpendicular to ba, we have : Aa : : bp : bA : : pq : A/3.
Hence, while A travels to a, and B to b, P travels to p. and thence to 7r. And the sines of the angles BAb and Aba. which are the angles of incidence and refraction, are to each other as Bb to Aa, i.e., as the.velocity in the first medium is to that in the second. See DIOPTRICS.
It is obvious from the cut that the less is the velocity in the second medium the more nearly does the refracted ray enter it at right angles to its surface. As a contrast we . _ . . . _ may introduce here a sketch of _Newton's admirable investigation of the same problem on the corpuscular hypothesis. Let AB (fig. 4) be the common surface of the two media, PQR the path of a corpuscle. Let U and V be the velocities in the two media, cr and t: the angles of incidence and refraction. Then the forces which ;Kit on the corpuscle being, entirely perpendicular to the refracting surface, the velocity parallel to that surface is not altered. This gives U sin. a = V sin. A Also the kinetic energy is increased by the loss of poten tial energy in passing from the one medium to the oilier. Hence the square of V exceeds that of U by a quantity depends only on the nature of the two media and of the corpuscle. This shows that V is the same what ever be the direction of the ray, and then the first rt la tion proves that the sines of the angles of incidence and reflection are inversely as the velocities in the two media, i.e., the refracting ray is more nearly perpendicular to
the refracting surface the greater is the velocity in the second medium. It is very singular that two theories so widely dissimilar should each give the true lab, of refraction; and in connection with what has just been said, it may be mentioned thatc n the corpuscular theory a corpuscle passes from one point to another with the least tier;0/2, while on the undulatory theory it passes in the least time. Hamilton's (q v.) grand prin ciple of varying action includes both of these.
Interference.—Fresners mode of exhibiting this phenomenon (whose discovery as before said is due to Young) is very simple and striking. An isosceles prism of with an angle very nearly 180°, is placed, as in fig. 5, symmetrically in limit of a bril liant point (the image of the sun formed by a lens of very short focus, for instance). The effect of the prism is that light which passes from 0 through the portion QR appears to have come from some point such as A (the image of 0 as seen through the upper half of the prism). Similarly the light which has passed through PQ appears to come from some point B. Thelight which has passed through the prism is to Le received on a white screen ST. At the point T, which is in the prolorurat ion of the line OQ. the distances TA and TB are equal; but for no other point. as U in the line ST, are UA and UB equal. Suppose U and V to be such that UA and UB differ in length by half a wave length of some particular color, VA and VB by a whole wave-length of the snme; waves arriving at T, as if from A and B, have passed over equal spaces. and conse quently their crests coincide, so that at T they re-euforee each other. But at U a Lnllow from A is met by a crest from B. so that earliness is the result. At V, again, (lest and crest coincide. And so on. Hence if we are experimenting with one definite color of light, the effect on the screen is to produce at T, V. etc., bright bands of that color, all parallel to the edges of the prism PQR. At points like U there are dark bands. And the length of a wave can easily be calculated from this experiment; for the lengths of OQ and QT can be measured, and knowing the angles of the prism and its refractive index (see REFRACTION) for the particular color employed. We Call calcu late the positions of A and B. We have then only to measure the disiance TV between the centers of the two adjoining bright bars, and then geometry enables its to calculate the difference of the lengths of VA and VB, which as we have seen is the length of a wave. The results of this experiment show how very minute are these wave-lengths for visible rays. Thus for Inch.