REFRACTION. When a ray of light passes out of one transparent medium into another of different density it is bent out of its course, and suffers deviation.
The law is, that the refracted ray lies in the same plane with the incident ray and the normal to the surface at the point of incidence ; and that it lies on the opposite side of the normal, and makes with the normal an angle of refraction the sine of which bears to the sine of the angle of incidence a constant ratio, depending on the nature of the two media.
When refraction takes place from vacuum into a medium, this constant ratio is called the " refractive index" of the medium, and is generally denoted by the Greek letter is . It is always greater than unity.
If then, be the angle of incidence S6' refraction the law of refraction is expressed by the equation sine 0=tt sine o' which is called the " Law of Sines." The sine of an angle is a decimal fraction less than unity, and may be found by consulting a table of natural sines. The sine of 0°=. 0 ; of 90°=1 ; of 30°=•5 ; and so on. See "Sine." Suppose then the refractive index of a piece of glass to be 1.54, and the angle of incidence of a ray upon its surface to be 37° 18'; required to find the angle of refraction.
By consulting the table we find that the sine of 37°18'= -60599 : Therefore x sine cp' which gives sine Consulting the table again, we find that •9341 is the natural sine of 23°10', and -39367 the natural sine of 23°11'; therefore the angle of refraction, c' is equal to 23°10' 20".
The following table gives the value of it for a few different sub stances.
Chromate of lead . . . 2.974 Diamond. . . . • . 2.439 Nitrate of silver . . . . 1.788 Flint glass . . . . .from 1.625 to 1.58 Crown glass . . . . from to 1.514 Canada balsam . . • . .1.55 Castor oil . . . . . . 1.49 Turpentine . . . . . 1.475 Nitric acid . . . . . 1.41 • Alcohol . . . . . 1.372
Acetic acid . . . . . 1.36 Ether . . . . . . 1.358 Water . . . . . . 1.335 Air . . . . . . 1.000276 We have now to consider the case of a ray about to pass from a dense medium into vacuum.
A ray of light on having its direc tion reversed returns by the same path as that by which it came ; so that if PNB be a vacuum, PnB a dense me dium, and pAq the bent course of a ray proceeding in the direction of the arrow, if this ray be reversed and turned back it will follow the course qAp. If then the angle pA N=f, and qAn=0',theequationsinef =tisine0' 1 becomes sine 0'= —sine 0.
If be such that =90°, sine will be equal to 1 —; and 1 the angle whose sine is — is called the " Critical Angle." Suppose, now, PA to be a ray whose angle of incidence differs from 90° by a quantity less than any assignable quantity ; it will then after refraction follow the course AQ, and QAn will be the "critical angle." This angle for plate glass is about 42°, and for flint glass about 39°, therefore less than 45° in both cases.
Now observe what follows :— Any ray within the dense medium, proceeding towards A and lying within the angle n Q, will emerge and take a direction somewhere ithin the angle PN ; but no ray incident at A whose direction lies within the angle QB will be able to get out of the glass, but will sutTer total reflexion, as shown in the figure by the ray LAM ; the angle L A n being equal to the angle M An.
The meaning and importance of the critical angle will now be per ceived ; for the inner surface of a transparent medium may become a totally reflecting surface ; and a block of transparent glass may be as perfectly opaque to light as a sheet of iron. It is on this princi ple that the reflecting prism is constructed; (g. v.).