The ratio of the sine of the angle of incidence to the sine of the angle of refraction, when a ray passes from one medium to another is termed the relative index of refraction. When a ray passes from vacuum into any medium, this ratio is always greater than unity, and is called the _absolute index of refraction_, or simply the index of refraction for the medium in question.
The absolute index of air is so small that it may be neglected in comparison with those of solids and liquids; but strictly speaking, the relative index for a ray passing from air into a given substance must be multiplied by the absolute index of the air, in order to obtain the true index of refraction.
[Illustration: Fig. 5.--Vision through a Glass Plate.]
=Critical Angle.=--It will be seen from the law of sines that, when the incident ray is in the less refractive of the two media, to every possible angle of incidence there is a corresponding angle of refraction. The angle referred to is termed the _critical angle_, and is readily computed if the relative index of refraction be given. When the media are air and water, this angle is about 48° 30′. For air and ordinary kinds of glass its value varies from 38° to 41°.
The phenomenon of total reflection may be observed in several familiar instances. For example, if a glass of water, with a spoon in it, is held above the level of the eye, the under side of the surface is seen to shine like a mirror, and the lower part of the spoon is seen reflected in it. Effects of the same kind are observed when a ray of sunlight passes into an aquarium--on the other hand rays falling normally on a uniform transparent plate of glass with parallel faces keep their course; but objects viewed obliquely through the same are displaced from their true position. Let S (Fig. 5) be a luminous point which sends light to an eye not directly opposite to it, on the other side of a parallel plate. The emergent rays which enter the eye are parallel to the incident rays; but as they have undergone lateral displacement, their point of concourse is changed from S to S′, and this is accordingly the image of S. The rays in such a case which compose the pencil that enters the eye will not exactly meet in any one point; there will be two focal lines, just as in the case of spherical mirrors. The displacement produced, as seen in the figure referred to above, increases with the thickness of the plate, its index of refraction, and the obliquity of incidence. This furnishes one of the simplest means of measuring the index of refraction of a glass substance, and is thus employed in Pichot’s refractometer (“Deschanel”).