# Bq Bc

## direction, refraction, wave-front, ordinary, bodies and waves

B'Q = B'C' sin (B'C'Q) and the angle = a,. and the angle B'C'Q = a, Hence the condition becomes sin a, sin rt, The velocity of any homogeneous train of waves in any one medium is constant (but varies with the medium) ; therefore for any such train of waves is — a constant and may be written n as before, the index of refraction of the second medium with reference to the first. Thus it is seen that the incident ray CC' become, C'C" by refraction, that they lie in a plane which includes the perpendicular to the surface at C', and that their angles of incidence and refraction are given by the formula a, where n is a constant for any one train of waves. Thus n, and there fore the velocity of ether-waves, may be found to vary both for different colors in one medium and for the same color in different media. since it has been shown that in ordinary matter n in crease, a, the color is changed from red to yellow, to green, to blue, etc., it is evident that the elueity of those waves which produce the sen sation red—'red waves'—is greater in ordinary matter than is the velocity of 'green waves,' etc. For if the first medium is the pure ether and the second air (or glass, or water), r, remains con stant for all waves. and if n increases it must he because r, decreases.

Double refraction is at once explained if the assumption is made that, whereas a point-souree in an isotropic medium produces a spherical wave-point, in media which have different prop erties in different directions a point-source pro duces a more complicated wave-front. To ex plain the simpler ease of double refraction, that where one ray obeys the ordinary laws of re fraction, Huygens assumed that the wave-front was a combination of a sphere and an ellipsoid of revolution, the axis of revolution being a diameter of the sphere. In bodies of this nature there is always one direction in which they be have in all respects like ordinary transparent bodies. This is called the 'optic axis.' and it is

evidently in the direction of the axis of revolu tion of the ellipsoid of the wave-front. (It is not a line, hut a direction; and so all lines drawn in this direction within the body are optic axes.) These bodies are therefore called 'uniaxial.' Let such a body have a face cut and polished making an angle 6+ with the optic axis. and let the paper make a section perpendicular to this face and including the optic axis. If a plane wave front ABC is incident on this face, the dis turbance at A in the uniaxial body sends out its doable wave-front. the section of whieb—a circle and an ellipse—is shown; and while the disturb ance goes from C to C' in the air let the double wave-front advance as shown. Then at this in stint the wave-fronts in the uniaxial body may be easily seen to be planes NN 11101 pass through the line peri•endieular to the paper at C' and are tangent to the sphere and to the ellipsoid. The disturbance from A ha, thus reached the points of tangency 0 and E. A)) and AE. are called the ordinary and the extraord inn Ty rayR; and it is evidtlit from geometry that the latter ray does not in general obey either of the last, of ordinary refraction. Two linos drawn perpen dicular to the wave-fronts, e.g. WI t' and WE', are called the wave 'normals;' and it is seen that in general the extraordinary ray does not have the same direction as the extraordinary wave normal, i.e. the ray is advancing in a direction different from the direction of advance of the wave-front. In other doubly refracting bodies there are two optic axes; such are called 'biaxial.' Fresnel explains their optical properties by as suming a peculiar kind of wave-surface, which is too complicated for description here.

The wave-surface of lluygens fur nniaxial bodies may be regarded as definitely established by experiment; while all that can be said in regard to Fresnel's wave-surface for biaxial bodies is that it is most probably correct.