LIGHT 591
into B, and /A., that for the same ray from A into C, that from B into C is .
Refraction by water.
These being premised, let us consider a source of homogeneous light in air shining on a surface of water. Here we may take p. as about equal to -.
Let MN (fig. 12) be the perpendicular to the water surface at the point where the incident ray AP meets it. In the plane APM make the angle QPX such that
then PQ is the refracted ray. If QP be produced back wards to meet the vertical line BA in q, we may present this statement in the form
PB PA . J Pq If the rays fall nearly perpendicu larly on the surface, we may put (ap proximately) B for P, and we have B? = JBA. Hence, an eye placed under water and nearly in the vertical through A, sees a virtual image of A at q, one-third farther from the surface of the water. As P is taken farther and farther from A, the angle of incidence becomes more nearly a right angle, and the sine of the angle of refraction becomes more nearly equal to f . A ray cannot go from air into ivater so as to make, ivith the perpendicular to the surface, an angle ivhose sine is greater than f. The true nature of this curious statement is, however, best seen when we suppose the source to be under water, and the light to be refracted into air. If APQ (fiy. 13) be the course of a ray, we have as before AP-*P ? . Hence, if P l be taken so that AP^iPjR, otal re- it is clear that q coincides with B, or the ray APj, refracted .exion. a t p^ runs a i on g the surface of the water. If AP., be less than -*- P 2 B, no point q can be found ; so that the ray AP., cannot get out of the miter. It is found to be completely reflected in the water. This reflexion unaccompanied by- refraction is called total reflexion. The limiting angle of incidence (at P x ) which separates the totally reflected rays
Critical angle.
from those which (at least partially) escape into air is called the critical angle. When an equilateral triangular prism of glass is placed in a ray of sunlight, and made to rotate, we see (besides the spectra formed by refraction) beams of white light reflected alternately from the outside and the inside of each face. The totally reflected ray from the inside is seen to be very much brighter than that reflected from the outside.
To an eye placed nearly in the vertical of A, A appears at A , where
Thus a clear stream, when we look vertically into it, Appear- appears to be of only |ths of its real depth. But when we an f e * look more and more obliquely, seeing A for instance by the ray QP, the image appears nearer and nearer to the surface ; water. or, if A be at the bottom, the water will appear more and more shallow; and all objects in it will appear to be crowded towards the surface. Thus the part of a stick immersed in water appears bent up towards the surface of the water.
Again, to an eye at A, all objects above the water will be seen within a right cone of which AB is the axis and APj a side. The rest of the water surface, outside the cone just mentioned, shows us objects at the bottom by reflexion in a perfect mirror.
All this is on the supposition that the light is homo geneous. But when white light is emitted by A, the point A will be nearer the surface for each constituent the greater is the refractive index. Thus a white point at A will appear drawn out into a coloured line whose lower end is red and upper end violet.
It is easily seen from the law of refraction that light, on passing through a plate of homogeneous material with parallel faces, finally emerges in a direction parallel to that at incidence, and therefore white light comes out from it still white. If the plate be water in a glass vessel with parallel sides, a body placed close to one side, while the eye is close to the other, appears to be at f ths of its real distance from the eye.
The explanation of the law of refraction, on the corpus- Corpus cular theory, was given by New^ton. It is still of import- cnl&r ance, as the earliest instance of the solution of a problem "plana- involving molecular forces. Xewton shows that, as the tlie ]aw molecular forces on a corpuscle balance one another at O f re- every point inside either of the media, its velocity must be fraction. constant in each, but that in passing through the surface of separation of the two media the square of the velocity perpendicular to the surface undergoes a finite change. Thus, if v be the velocity in air, a the angle of incidence, then in glass the velocity parallel to the surface is still v sin o, but that perpendicular to the surface is fv-cos~a. + a-. Thus the whole velocity is V J + a 2 ; and, if o be the angle of refraction,
v- + a 2 sin a = v sin a.
Prisms.- "When the surfaces are plane, but not parallel, Prism. we have what is called a prism. The general nature of the action of a prism will be easily understood by the help of the previous illustrations, if we restrict ourselves to the case of a prism of very small angle and to rays passing nearly perpendicular to each of its faces. Thus, the rays falling nearly at right angles to its surface from a point A (fig. 14) will, after the first refrac tion, appear to diverge from aluminous line RV, red at the end next to A, violet at the other. This line is in the perpendicular AB from A to the first surface of the prism. Draw from R and V perpendiculars RS, YT to the second surface of the prism. Join BS, BT, and draw Ar, Av parallel to them so as to cut RS in r and VT in v. To an eye behind the prism, the bright point A will appear to be drawn out into a coloured line rv, red at the end nearest to A.
