CHAPTER II.

REFLEXION AND REFRACTION.

(20) WHEN light meets the surface of a new medium, a portion of it is always turned back, or reflected.

The reflexion of light is twofold. Thus, when a beam of solar light is admitted into a darkened chamber through an aperture in the window, and is allowed to fall upon a metallic mirror, a reflected beam is seen pursuing a determinate direction after leaving the mirror; and if the eye be placed in this direction, it will perceive a brilliant image of the sun. This beam is said to be regularly reflected, and its intensity increases with the polish of the mirror. But it is observed also, that in whatever part of the room the eye is placed, it can always distinguish the portion of the mirror which reflects the light; some of the rays, consequently, are reflected in all directions. This portion of the light is said to be irregularly reflected, and its intensity decreases with the polish of the mirror.

Irregular reflexion is due, mainly, to the inequalities of the reflecting surface, which is composed of an indefinite number of reflecting surfaces in various positions, and which therefore reflect the light in various directions.

(21) The angles of incidence and reflexion (or the angles which the incident and reflected rays make with the perpendicular to the reflecting surface at the point of incidence) are in the same plane, and are equal. This law is universally true, whatever be the nature of the light itself, or that of the body which reflects it.

(22) The intensity of the reflected light, on the other hand,

C

is found to vary greatly with the medium. The following leading facts have been established experimentally.

I. The quantity of light regularly reflected increases with the angle of incidence, the increase being very slow at moderate incidences, and becoming very rapid at great ones. Thus, water at a perpendicular incidence, according to the experiments of Bouguer, reflects only 18 rays out of 1000; at an incidence of 40° it reflects 22 rays; at 60°, 65 rays; at 80°, 333 rays; and at 8940, 721 rays.

II. The quantity of light reflected at the same incidence varies both with the medium upon which the light falls, and with that from which it is incident. Thus, at a perpendicular incidence, the number of rays reflected by water, glass, and mercury, are 18, 25, and 666, respectively, the number of incident rays being 1000. The dependence of the quantity of the reflected light upon the medium from which it is incident is easily shown by immersing a plate of glass in water or oil.

III. The differences in the reflective powers of different substances are much more marked at small, than at great incidences. Thus, water and mercury-the first of which reflects but the one-fiftieth part of the incident light at a perpendicular incidence, while the latter reflects two-thirds -are equally reflective at an incidence of 89°, the number of rays reflected at this angle being, in both cases, 721 out of

1000.

(23) When light is incident upon the surface of a transparent medium, a portion enters the medium, pursuing there an altered direction. This portion is said to be refracted.

When the ray passes from a rarer into a denser medium, the angle of incidence is, in general, greater than the angle of refraction, and the deviation takes place towards the perpendi cular to the bounding surface. On the contrary, when the ray passes from a denser into a rarer medium, the angle of

ncidence is less than the angle of refraction, and the deviaion is from the perpendicular.

(24) The angles of incidence and refraction are in the same lane; and their sines are in an invariable ratio.

In order to verify this law experimentally, it is only necesary to measure several angles of incidence at the surface of he same medium, and the corresponding angles of refraction. This was done by Ptolemy in the second century, and subsequently by Vitello in the thirteenth; but both of these observers failed in discovering the connecting law. The law of efraction, just stated, was discovered by Willebrord Snell, bout the year 1621.

If and be employed to denote the angles which the portions of the ray in the rarer and denser medium, respectively, make with the perpendicular to the common surface, the second part of the law of refraction is expressed by the equation,

sin,

sin = μ sin 4,

u being a constant quantity. This constant is termed the index of refraction; and since p > 4, it is always greater than unity.

When a ray of light passes into any medium from a vacuum, the index of refraction is in that case termed the absolute index of the medium. For air, and the gases, it exceeds unity by a very small fraction; for water, μ = 1.336; for crown glass, μ 1.535; for diamond, μ 2.487; and, for chromate of lead, μ = 3.

=

με

=

(25) When light traverses a prism,—that is, a medium bounded by two inclined plane surfaces, the total deviation of the refracted ray is the sum of the deviations at incidence and emergence. Let Φ and p' denote the angles which the inci1 dent and emergent rays make with the perpendiculars to the faces at the points of incidence and emergence, and the

angles which the portion of the ray within the prism forms with the same, then the deviations at incidence and emergence are, respectively, 4, and '-'; and the total deviation 8 = p + p' − (↓ + 4). Now, it is easily shown that the alge braic sum of the angles, which the portion of the ray within the prism makes with the two perpendiculars, is equal to the vertical angle of the prism; or, denoting this angle by a, that

(26) When a ray of light is incident nearly perpendi cularly upon a thin prism, the total deviation is constant, and bears an invariable ratio to the angle of the prism.

For in this case the angles of incidence and refraction, being small, are proportional to their sines, so that

Hence

φ=μψ, φ' = μψ'; and φ + φ' = μ (4+4) = μα.

(27) The deviation produced by a prism is easily deter mined when the angles of incidence and emergence are equal For we have seen that, generally,

=

But since, in this case, p=p', there is also '; and con sequently

$ = 1/2 (a + d),

4 = a.

from which a + 8, and therefore 8, is determined.

It may be shown that the angle of deviation, in this cas is the least possible; and accordingly, if the prism be turne slowly round its axis, the inclination of the emergent to t incident ray will first decrease, and afterwards increase, a

pearing for a moment to be stationary between the opposite changes. By this principle it is easy to place a prism, experimentally, in the position in which the refractions are equal at both sides.

(28) We are now enabled to determine the refractive index of a transparent solid experimentally.

The first step of this process is to polish two plane faces, inclined to one another at a sufficient angle, and to measure that angle by a goniometer. This being done, the prism is to be placed, with its refracting edge vertical, before the objectglass of the telescope of a theodolite, so as to refract to the cross wires in its focus the rays proceeding from a distant mark. The prism is then to be turned slowly round its axis, and the telescope moved, until the deviation is a minimum. The horizontal circle being read, and the prism removed, the telescope is to be turned directly to the distant mark, and the reading repeated; the difference of the two readings is the deviation. The angle of the prism and the deviation being obtained, the refractive index is given by the formula,

To determine the refractive index of a fluid, we have only to inclose it in a hollow prism, whose sides are formed of glass plates with parallel surfaces. For the course of the ray will be the same as if it had been incident directly from the air into the fluid, and had emerged similarly, without passing through the glass.

(29) Let us now proceed to the physical explanation of the phenomena.

To account for the phenomena of reflexion and refraction, it is supposed, in the theory of emission, that the particles of bodies and those of light exert a mutual action ;-that, when they are nearly in contact, this action is attractive ;—that, at