DIOP'TRICS is that branch of geometrical optics (see OPTICS) which treats of tho transmission of rays of light from one medium into another, differing in kind. It consists of the results of the application of geometry to ascertain in particular cases the action of what are called the laws of refraction. When a ray of homogeneous light is incident upon a surface, the angle which its direction makes with the normal or per pendicular to the surface at the point of incidence is in D., as in catoptrics, called the angle of incidence. The angle which the refracted ray makes with the same line is called the angle of refraction. This being premised, we may state the laws of refrac tion. 1. The incident and refracted ray lie in the same plane with the normal, at the point of incidence, and on opposite sides of it. 2. The sine of the angle of incidence, whatever that angle may be, bears to the sine of the angle of refraction a constant ratio dependent only on the nature of the media between which the refraction takes place, and on the nature of the light. According to the second law, if we call the angle of incidence 7; and that of refraction r, we shall have sin i = p sin r, where p is a quantity depending upon the nature of the media and of the light. It will have, for instance, a certain value for refraction from vacuum into glass, another from glass into water, and so on; also, it will have one value for red light, another for green, and so on. The quantity p is called the refractive. index.•and is greater than 1 when refraction takes place from vacuum into a medium, and in general is greater than 1 when the refraction is from a rarer into a denser medium, and Tess than 1 when the opposite is the case. In D., the laws of refraction may be considered as depending for their truth upon experiment; in physical optics, they are deductions from an hypothesis respecting the constitution of light. They are not merely approximately true; they are absolute phys ical laws.
Before proceeding to consider the simpler leading cases of refraction, one or two interesting propositions in dioptrics require to be explained.-1. If the refractive index for a medium, when light is incident upon it from vacuum, be u, and the index for another medium, under the same circumstances, be /L', then, when light proceeds from the second medium into the first, the refractive index is – The proof of this proposi tion depends upon the two following experimental laws; (1.) If a ray of light proceed front a point to a second, suffering any reflections or refractions in its course, then, if it be incident in the reverse direction, i.e., from the second point,•it will follow the exactly
reverse course to the first point. This is proved by experiment, but may be accepted as axiomatic. (2.) If a ray pass from vacuum through any number of media, having their faces plane and parallel, when the ray emerges into vacuum its direction will be parallel to that which it had before incidence. To deduce the proposition from these laws, let i be the angle of incidence from vacuum upon the first medium, r the angle of refraction, which will also be the angle of incidence upon the second medium. Also let r' he the angle of refraction into the second medium, which will also be the angle of incidence upon the second bounding surface. By the second of the experi mental laws, the angle of emergence into vacuum will be i. Hence we shall have by the first of these laws, sin i = p' sin r at the first surface, and sin i = u sin r' at the second. From these equations, we have sin r = — sin r, which proves the proposition. It follows that if it be the refractive index from vacuum into a medium, that from the medium into vacuum will be Our second proposition relates to what is called the critical angle. If i be the angle of incidence of a ray within a medium, the refractive index of which is p, and r the angle of refraction into vacuum, then we have from the former proposition sin i = sin r. From this formula, if i be given, r may be found, and a real value will be given to r so long as sin i is Z but when ilias a value greater than that determined by the equation sin i = the formula fails to give us a value of r, for the sine of an angle cannot be greater than 1. And experiment shows that, in fact! there is no refracted ray when the angle of incidence is greater than that above assigned, the ray being wholly reflected within the medium. The angle of which the sine is is called the critical angle. For glass, it is about 41° 45'; for water, about 48' 30'. This angle is sometimes called the angle of total reflection. In internal reflection at the surfaces of media, the reflected light is more nearly equal in intensity to the inci-• dent than in any other case of reflection. While it thus appears that refraction from a denser into a rarer medium is not always possible, it may be added, that it is always possible from a rarer into a denser.