Page:The American Cyclopædia (1879) Volume X.djvu/445

 LIGHT 439 dia generally, air is considered as the first me- dium. The indices of refraction for various substances are given in the following table, and are calculated for yellow light, except those marked *, which are for extreme red : TABLE OF INDICES OF KEFKACTION. SUBSTANCE. Ind. of refr. SUBSTANCE. Ind. of refr. Crown glass Flint glass 1-534 1-570 Kuby Feldspar 1-779 1-764 Kock crystal* Kock salt 1-547 1-545 Tourmaline Diamond 1-668 2-500 Canada balsam 1-582 Phosphorus 2-224 Sugar* 1-585 Sulphide of carbon 1-678 Spermaceti Borax 1-503 1-475 Linseed oil* Olive oil 1-485 1-470 Alum* 1-457 Oil of turpentine*. 1-470 Fluor spar. ... 1-436 Alcohol 1-872 Emerald 1-585 Ether 1-358 The phenomena of reflection and refraction are explained on the emission theory by supposing that the projected luminous particles and the particles of bodies exert a mutual action, either repulsive or attractive. In certain positions the particles of light are supposed to be re- pelled, and therefore reflected ; in other posi- tions they are attracted, and therefore pass into the medium and are refracted. In the wave theory it is supposed that when a wave of light reaches the surface of a second medi- um whose elasticity is different, it gives rise to two waves, one in each medium, both differ- ing in position from the original wave. But the several portions of the incident wave will reach the surface at different moments of time, and each of these portions will be the cen- tre of two new waves, one of which will be propagated in the first medium with the ve- locity of the incident ray, and the other in the second medium with a velocity depending on the density of the ethereal particles within it ; so that an infinite number of partial waves will be reflected and refracted, forming by their union grand or primary wave fronts at right angles with the reflected or refracted rays. The following is a condensation of the elegant demonstration of Huygens. Let a e, fig. 4, be the front of a plane wave meeting the reflecting surface at a. As each portion of this wave reaches the surface, it becomes the centre of a spherical wave in the first medium having the same velocity. Therefore, when the portion e has reached the surface at c, the portion a will have formed a spherical wave whose radius a m is equal to e c, and the portion 5 will also have formed a wave whose radius 5 o is equal to d c. The surface n m e, which touch- es all these partial wave fronts, is the front of the reflected wave ; but since a e and 5 o are proportional to a c and 5 c, it follows that this surface is plane ; and furthermore, since a m= e c, and the angles at e and m are right angles, FIG. 4. the angles e a c and m c a are equal, or the in- cident and reflected wave fronts (and there- fore the rays) are equally inclined to the re- flecting surface. The demonstration of the law of refraction is similar. If a e, fig. 5, is the front of a plane wave, when the portion a reaches the sur- face a partial wave is generated, which will proceed a cer- tain distance, while the portion e pass- es on to c, and the portion g will ar- rive at &, where a partial wave is also generated, with the FIG. 5. same velocity as that formed at a. As these partial waves form a plane wave front in the refracting medium, their direction must be such that they will reach the plane c n in the same time that the portions g and e reach I and c respectively ; and as sin e a c : sin a c o : : e c : a o (the an- gles at e and o being right angles), it follows that the sines of the angles are in the constant ratio of the velocities of propagation in the two media. The composition of the primary wave by the union of the several secondary waves in this demonstration has been called the "principle of Huygens," and is frequently employed in explaining many of the phe- nomena of light. Refraction produces some well known effects. When an object im- mersed in water is viewed obliquely, it appears nearer the surface than it really is, because the light in passing from the denser to the rare'r medium, or to that whose refractive in- dex is the less, takes a direction from the per- pendicular, or more inclined to a horizontal direction. When a ray of light enters a less refracting medium, there is always a value of the angle HOB, fig. 6, which causes the an- gle of refraction A O to be a right angle. If the angle of incidence H O B is increased, as to E O B, the ray cannot emerge from the first medium, but will be reflected from its internal surface. The angle H O B is therefore called the critical angle, and its sine is the recipro- cal of the index of re- fraction of the medium. From water to air this critical angle is 48 35', and from glass to air it ranges from 38 to 42. From the diamond to air it is only 24, leaving a range of 66 in which re- flection takes place from the internal surfaces of the faces of the crystal ; to which circumstance this gem owes its brilliancy and splendid play of colors. The phenomenon of mirage depends upon the unequal refractive powers of the dif- ferent strata of the atmosphere in consequence of the different quantities of vapor which they FIG. 6.