99.]

REFLECTION FROM CURVED SURFACES.

169

tially covered with clouds, and the strong lights which fatigue the eyesight in a cloudless summer's day. It is entirely to this secondary radiation that we owe the generally diffused and subdued light of day, even when the sun itself may be concealed by clouds; and the morning and evening twilight, while the great luminary itself is below the horizon, is due to the same cause, each illuminated particle of the atmosphere contributing its share in producing this effect.

(98) Reflection from Curved Surfaces.-When light is received upon a regular curved surface, it undergoes reflection according to the usual law, the reflection from each point of the curved surface being, in fact, the same as from a plane, tangent to the curve at the point of incidence. If, therefore, the form of a parabolic concavity be given to a mirror, and light in parallel rays be allowed to fall upon its surface, all the reflected rays will be directed towards a point at which they will cross each other, and continue their progress as before, the upper ray now becoming undermost, and vice versa. This point of intersection is called the focus of the mirror.

respective rays; they will consequently meet at the focus F, cross there, and subsequently diverge.

perpendicular to the tangents.

PR, PR represent the lines

(99) Simple Refraction.-When a ray of light falls upon the surface of an uncrystallized transparent substance of uniform density, one portion of the light is regularly reflected, and another portion is scattered, by which the surface is rendered visible, whilst a third portion is transmitted. We will now confine our

attention to that portion of the light which is transmitted. If the ray be incident upon the surface of the body in a perpendicular direction, it continues its course unchanged; but if it fall upon the surface obliquely, its direction is suddenly altered as it

170

FIG. 71.

SIMPLE REFRACTION OF LIGHT.

[99.

enters the transparent medium; it then passes on in its new direction in a straight line, and on quitting the medium it is. again abruptly bent back and rendered parallel to its original course, provided that the surface of entrance and the surface of exit be parallel to each other. This change in the course of the ray is termed refraction. If, in fig. 71, G G represent a section of a plate of glass with parallel sides, a ray of light, 1 L, incident obliquely upon it, does not pass straight on in the direction L X, but is deflected to LR, towards the perpendicular, P Q; on quitting the medium at R, it is again bent out of its new direction, L Y, towards S, but this time the refraction is from the perpendicular, R O, and the ray, R s, becomes parallel to its original course, I X. On passing from a medium like air, into another like glass, the ray is bent towards a line perpendicular to the common surface of the two media; on again passing out from glass into air; or from a more refracting to a less refracting medium, it is bent from the perpendicular to the same amount. The cause of refraction is the diminution of velocity with which light passes through more powerfully refracting bodies (113).

R

Different media vary greatly in refracting power; combustible bodies in general having the highest refracting energy. It was upon this general observation that Newton founded his conjecture that diamond was 'probably an unctuous substance coagulated'; the combustibility of the diamond has been since fully verified.

(100) Law of Refraction.-The more obliquely the light falls upon the surface of the refracting body the greater is the amount of refraction which the ray experiences. The extent of the refraction, therefore, varies with the angle of incidence, but by a knowledge of the following law it may easily be calculated for all angles in any given substance, if its amount for any one angle has been carefully determined for that particular substance. This law of refraction may be expressed by stating that when light passes from one medium into another, for the same two media, the sines of the angles of refraction and of incidence always bear the same ratio to each other.' The quotient obtained by dividing the sine of the angle of incidence in vacuo by the sine of the angle of refraction in any medium, expresses the index of

100.]

REFRACTION-LAW OF THE SINES.

171

refraction of that medium. The incident and the refracted ray are always on opposite sides of a line drawn perpendicular to the common surface of the two media, but they always lie in the same plane, and this plane is perpendicular to the surface of the refracting medium.

Fig. 72 may assist in explaining this important law. Let w w represent a section of the refracting medium, I L the incident ray, and L R the refracted one. Let PLQ be the perpendicular to the refracting surface, passing through the point of incidence, L. With any radius, L R, describe from the centre, L, the circle, R M P; from м and R let fall the perpendiculars м N and R Q, on P Q; MN will then represent the sine of the

MN

RQ

M

FIG. 72.

N

M

angle of incidence, I L P, and R Q the sine of the angle of refraction, R L Q; and gives the index of refraction, which is uniformly the same for the same substance, whatever be the angle of incidence. In the diamond, for instance, м N is always 2 times as long as RQ; in water it is 1 times the length of R Q.

The following table contains the indices of refraction of a few substances; the light being supposed to pass from atmospheric air :

The examination of the refracting power of bodies in their gaseous, or least complex molecular condition, possesses a special interest; the subject was first investigated by Biot and Arago, and it was carried further by Dulong. (Ann. Chim. Phys. 1826 [2], xxxi. 154.)

It appears that there is no simple relation between the refracting power of gases and their densities. The vapour of hydrochloric ether, for example, differs but little in density from sulphurous anhydride, though the refracting power of the former body is nearly two-thirds greater than that of the latter and ordinary ether has more than double the refracting power of chlorine, though their densities in the aëriform state are nearly the same.

:

The refracting power of a gas or of a vapour is proportioned to the pressure, and is not affected by temperature, at least so far as experiments on pressures not greater than that of one atmosphere, and on temperatures ranging between 7° and 38° C. can decide the question. The refracting power of a mixture of gases is equal to the sum of that of its constituents calculated for the pressure of each constituent in proportion to the amount present in the mixture. But the refracting power of a compound may be either greater or less than that of the sum of its constituents.

More recently Le Roux (Ann. Chim. Phys. 1861 [3], lxi. 385) has extended

172

REFRACTIVE POWER OF GASES.

2-1

[100. those observations to the vapours of certain simple substances which can only be volatilized at elevated temperatures. He, found the refringent energy ("2-1, μ being the index of refraction and d the vapour density) of sulphur vapour to agree with that of oxygen as determined by Dulong, and that of the vapour of phosphorus agreed closely with a similar determination for nitrogen. It is possible that these coincidents are only accidental, for elements which are analogous in their chemical relations have not been found to exhibit generally any close agreement in refracting power.

μ

Le Roux remarks that in the case of gaseous bodies it is a matter of indifference whether the refringent energy be calculated from the formula or ; since the index of refraction μ is of the form I + e, e being a very small quantity; consequently its square will be equal to 1 + 2e within a quantity certainly less than that due to errors of observation.

d

The following table exhibits the principal results of the experiments of Dulong, the four last being due to Le Roux. The refracting power of each gas as compared with air is calculated upon the supposition that they are all under a pressure of 760mm. at o° C.

Many familiar phenomena receive an easy explanation from the law of refraction. If a coin be placed in an opaque vessel, and the observer retire until the edge of the basin just hides it from his view, the coin will again become visible if water be carefully

* These densities have since in many cases received corrections.

102.]

REFRACTION AT INCLINED SURFACES.

173

poured in without disturbing its position; the rays of light proceeding from the coin, which before passed above the eye of the observer, are now abruptly bent downwards from the perpendicular, as they emerge into the air, and the image of the object is conveyed to the eye. The coin appears to be raised, but never displaced to the right or to the left of its true position; the refracted ray, notwithstanding its change of medium, continues in the same plane, which is vertical to that forming the common surface of the refracting media. For a similar reason a straight stick plunged obliquely into water appears to be bent upwards abruptly, where it enters the liquid.

(101) Refraction at Inclined Surfaces.-Since the refraction is exercised at the surface of junction between the two media, and is governed by the inclination of the ray to a perpendicular to that surface, it is manifest that by altering the inclination of the surface at which the ray passes out of the medium, the inclination of the emerging ray may be altered; so that, instead of continuing its passage in a direction parallel to the one which it possessed on entrance, it may be made to deviate permanently from this to a greater or less extent.

If G G G (fig. 73) represent the section of a triangular prism, or bar of glass, the incident ray, I L, on entering this medium is bent towards the perpendicular, P P : on quitting it at R, it is bent from the perpendicular, Q P, and assumes a course, R 8, permanently deflected from its new direction, I Y, and from its original direction, IX. This deflection is always

FIG. 73.

L

towards the thick part of the prism. By employing two such prisms set base to base, the rays may be refracted towards one common line, where they would cross and diverge; and by using a lens of glass (fig. 74), with two convex surfaces, which are segments of spheres, the incident rays R L, R L, may be caused to converge towards a common focus F; each portion of the curved surface refracting the ray in the manner of a plane, т T, TT, TT', tangent to the curve at that particular spot or point of incidence.

(102) Total Reflection.-In the passage of light from a more