When the polish of the surface is such that the irregularly scattered rays bear but a small proportion to the regularly reflected light, we become then principally sensible of the effects of the latter in pro ducing images of all the bodies of which the incident light is reflected to the eye : we are thus led to consider the laws of regular reflection.
Let An represent a surface of mercury at rest, and therefore perfectly horizontal ; E T the axis or line of collimation of a telescope, by which we perceive a the image by reflection of the star 9, and let the angle A Ca of its apparent depression below the horizon be measured. Then, turning the telescope in the vertical plane z c E until its line of colli mation takes a position T' E, in which the star itself becomes visible, and measuring its apparent zenith distance T' E z' or s c z, this angle is found invariably to be the complement of the former angle A Cs. Now, z c m being the complement of A o a or T c 13, it follows that the angles z c s, z o T are equal.
This experiment demonstrates that the reflected ray o T is in the same plane z c s as the incident ray c s and the normal o z, and that the angle formed by the reflected ray c T and the perpendicular to the surface—that is, T o Z, or the angle of reflection—is equal to s o z, the angle of incidence. Such are the laws which govern the reflection of light.
Let us suppose that light consists of a succession of particles emitted from the luminous body at intervals sufficiently short to produce vision, which hypothesis is generally known as that of emission ; then the pre ceding law would result from the supposition that the luminous mole cules, on approaching and entering the reflecting medium, are subject to forces proceeding from this medium, and of which the resultant is normal to the surface. For conceive the velocity of the luminous particle as it enters the medium—or rather, as soon as it comes within the influence of its forces, to be decomposed into one parallel and one normal to it. The force of the medium can exercise no influence on the former, and it is therefore the same at the exit of the ray from the influence of the medium as at its entrance. Again, the effect of the normal force on the square of the normal velocity in a space small enough to consider the force uniform, is the product of twice this force and the small interval of space, and it is therefore the same in increasing this quantity for the returning as in diminishing it for the incident ray ; and therefore the normal velocities of the incident and reflected rays are equal, as well as the parallel ; from whence it neces sarily follows that the angles of incidence and reflection are equaL It admits of easy geometric demonstration that the path of the ray between any fixed points in the incident and reflected parts is a mini mum (neglecting the insensible curvilinear part), in reference to any other supposed positions of these rays, when the reflecting surface is plane, or any curved surface which is tangent externally at the point of incidence to a spheroid having the fixed points for foci, and the length of the ray between them as axis major; for thew touching the aphereid internally it is a maximum.
If we 'uprose that light is propagated by undulations in a rare elastic medium from the luminous point as an origin, the velocity of the sayer, after reflection, is the sane as before incidence, since the medium is the woe; and hence, as in sound, the angle of reflection would still be the same as that of incidence. (Ecno.) Thus both the hypotheses of entisaicn and of undulations satisfactorily ac aunt for this fundamental law.
If the refloated ray of light were transformed to an incident, reciprocally the path of the incident would bet:nine that of the reflected. The Nano is true for any number of refleetions at different surfaces.
The deviation of a raw of light, after It has undergone any alteration in its muse by the action of media, is the inclination of the primitive and final directions of the ray taken in the sense in which they are moving. This deviation by one reflection on any surface is the supple ment of double the aught of incidence, or Is the double of the inclination of either ray to the medium.
A plane of rerfortion contains a successive incident and reflected ray, and is noosuarily perpendicular to the corresponding reflecting surface.