REFRACTION (Lat. refringere, to break open or apart), in physics, the change in the direction of a wave of light, heat or sound which occurs when such a wave passes from one medium into another of different density.
I. REFRACTION OF LIGHT
When a ray of light traversing a homogeneous medium falls on the bounding surface of another transparent homogeneous
medium, it is found that the direction of the transmitted ray in the second medium is different from that of the incident ray; in other words, the ray is refracted or bent at the point of incidence. The laws governing refraction are: (I) the refracted and incident rays are coplanar with the normal to the refracting surface at the point of incidence, and (2) the ratio of the sines of the angles between the normal and the incident and refracted rays is constant for the two media, but depends on the nature of the light employed, i.e. on its wave length. This constant is called the relative refractive index of the second medium, and may be denoted by /sob, the suffix ab signifying that the light passes from medium a to medium b; similarly µba denotes the relative refractive index of a with regard to b. The absolute refractive index is the index when the first medium is a vacuum. Elementary phenomena in refraction, such as the apparent bending of a stick when partially immersed in water, were observed in very remote times, but the laws, as stated above, were first grasped in the I'i th century by W. Snell and published by Descartes, the full importance of the dependence of the refractive index on the nature of the light employed being first thoroughly realized by Newton in his famous prismatic decomposition of white light into a coloured spectrum. Newton gave a theoretical interpretation of these laws on the basis of his corpuscular theory, as did also Huygens on the wave theory (see LIGHT, II. Theory of). In this article we only consider refractions at plane surfaces, refraction at spherical surfaces being treated under LENS. The geometrical theory will be followed, the wave theory being treated in LIGHT, DIFFRACTION and DIs-PERSION.
Refraction at a Plane Surface.—Let LM (fig. I) be the surface
dividing two homogeneous -media A and B ; let IO be a ray in the first medium incident on LM at 0, and let OR be the refracted ray. Draw the normal POQ. Then by Snell's law we have invariably sin IOP/sin QOR=µab. Hence if two of these quantities be given the third can be calculated. The commonest question is: Given the incident ray and the refractive index to construct the refracted ray. A simple construction is to take along the incident ray 01, unit distance OC, and a distance OD equal to the refractive index in the same units. Draw CE perpendicular to LM, and draw an arc with centre 0 and radius OD, cutting CE in E. Then EO produced downwards is the refracted ray. The proof is left to the reader.
In the figure the given incident ray is assumed to be passing from a less dense to a denser medium, and it is seen by the construction or by examining the formula sin fl= sin a/a that for all values of a there is a corresponding value of f3. Consider the case when the light passes from a denser to a less dense medium. In the equation sin 13= sin a/a we have in this case p I and there is no refraction into the second medium, the rays being totally reflected back into the first medium; this is called total internal reflection.
Images produced by Refraction at Plane Surfaces.—If a luminous point be situated in a medium separated from one of less density by a plane surface, the ray normal to this surface will be unrefracted, whilst the others will undergo - refraction according to their angles of emergence. If the rays in the less dense medium be produced into the denser medium, they envelop a caustic, but by restricting ourselves to a small area about the normal ray it is seen that they intersect this ray in a point which is the geometrical
image of the luminous source. The position of this point can be
easily determined. If l be the distance of the source below the by a lens L. Beneath the prisms is a mirror for reflecting light surface, 1' the distance of the image, and ,u the refractive index,
then 1'=I/n. This theory provides a convenient method for determining the refractive index of a plate. A micrometer microscope, with vertical motion, is focused on a scratch on the surface of its stage; the plate, which has a fine scratch on its upper surface, is now introduced, and the microscope is successively focused on the scratch on the stage as viewed- through the plate, and on the scratch on the plate. The difference between the first and third readings gives the thickness of the plate, corresponding to 1 above, and between the second and third readings the depth of the image, corresponding to 1'.
Refraction by a Prism.—In optics a prism is a piece of trans-parent material bounded by two plane faces which meet at a definite angle, called the refracting angle of the prism, in a straight line called the edge of the prism; a section perpendicular to the edge is called a principal section. Parallel rays, refracted successively at the two faces, emerge from the prism as a system of parallel rays, but the direction is altered by an amount called the deviation. The deviation depends on the angles of incidence and emergence; but, since the course of a ray may always be reversed, there must be a stationary value, either a maximum or minimum, when the ray traverses the prism symmetrically, i.e. when the angles of incidence and emergence are equal. As a matter of fact, it is a minimum, and the position is called the angle of minimum deviation. The relation between the minimum deviation D, the angle of the prism i, and the refractive index p is found as follows. Let in fig. 2, PQRS be the course of the
ray through the prism; the internal angles each equal
and the angles of incidence and emergence ' are each equal and connected with 4' by Snell's law, i.e. sin ¢ =n sin 0'. Also the deviation D is 2 (0-0'). Hence µ=sin (p/sin =sine (D+i)/sinli.
Refractomelers.—Instruments for determining the refractive indices of media are termed refractometers.
The simplest are really spectrometers, consisting of a glass prism, usually hollow and fitted with accurately parallel glass sides, mounted on a table which carries a fixed collimation tube and a movable observing tube, the motion of the latter being recorded on a graduated circle. The collimation tube has a narrow adjustable Flit at its outer end and a lens at the nearer end, so that the light leaves the tube as a parallel beam. The refracting angle of the prism, i in our previous notation, is deter-mined by placing the prism with its refracting edge towards the collimator, and observing when the reflections of the slit in the two prism faces coincide with the cross-wires in the observing telescope; half the angle between these two positions gives i. To determine the position of minimum deviation, or D, the prism is removed, and the observing telescope is brought into line with the slit; in this position the graduation is read. The prism is replaced, and the telescope moved until it catches the refracted rays. The prism is now turned about a vertical axis until a position is found when the telescope has to be moved towards the collimator in order to catch the rays; this operation sets the prism at the angle of minimum deviation. The refractive index p is calculated from the formula given above.
More readily manipulated and of superior accuracy are refractometers depending on total reflection. The Abbe refractometer (fig. 3) essentially consists of a double Abbe prism AB to contain the substance to be experimented with; and a telescope F to observe the border line of the total reflection. The prisms, which are right-angled and made of the same flint glass, are mounted in a hinged frame such that the lower prism, which is used for purposes of illumination, can be locked so that the hypothenuse faces are distant by about 0.15 mm., or rotated away from the upper prism. The double prism is used in examining liquids, a few drops being placed between the prisms; the single prism is used when solids or plastic bodies are employed. The mount is capable of rotation about a horizontal axis by an alidade J. The telescope is provided with a reticule, which can be brought into exact coincidence with the observed border line, and is rigidly fastened to a sector
S graduated directly in refractive indices. The reading is effected
into the apparatus. To use the apparatus, the liquid having been inserted between the prisms, or the solid attached by its own adhesiveness or by a drop of monobromnaphthalene to the upper prism, the prism case is rotated until the field of view consists of a light and dark portion, and the border line is now brought into coincidence with the reticule of the telescope. In using a lamp or daylight this border is coloured, and hence a compensator, consisting of two equal Amici prisms, is placed between the objective and the prisms. These Amici prisms can be rotated, in opposite directions, until they produce a dispersion opposite in sign to that originally seen, and hence the border line now appears perfectly sharp and colourless. When at zero the alidade corresponds to a refractive index of 1.3, and any other reading gives the corresponding index correct to about 2 units in the 4th decimal place. Since temperature markedly affects the refractive index, this apparatus is provided with a device for heating the prisms. Figs. 4 and 5 show the course of the rays when a solid and liquid
are being experimented with. Dr R. Wollny's butter refractometer, also made by Zeiss, is constructed similarly to Abbe's form, with the exception that the prism casing is rigidly attached to the telescope, and the observation made by noting the point where the border line intersects an appropriately graduated scale in the focal plane of the telescope objective, fractions being read by a micrometer screw attached to the objective. This apparatus is also provided with an arrangement for heating.
This method of reading is also employed in Zeiss's " dipping refractometer " (fig. 6). This instrument consists of a telescope R having at its lower end a prism P with a refracting angle of 63°, above which and below the objective is a movable compensator A for purposes of annulling the dispersion about the border line. Ia
the focal plane of the objective 0 there is a scale Sc, exact reading being made by a micrometer Z. If a large quantity of liquid be
available it is sufficient to dip the refractometer perpendicularly into a beaker containing the liquid and to transmit light into the instrument by means of a mirror. If only a smaller quantity be available, it is enclosed in a metal beaker M, which forms an extension of the instrument, and the liquid is retained there by a plate D. The instrument is now placed in a trough B, containing water and having one side of ground glass G; light is reflected into the refractometer by means of a mirror S outside this trough. An accuracy of 3.7 units in the 5th decimal place is obtainable.
The Pulfrich refractometer is also largely used, especially for liquids. It consists essentially of a right-angled glass prism placed on a metal foundation with the faces at right angles horizontal and vertical, the hypothenuse face being on the support. The horizontal face is fitted with a small cylindrical vessel to hold the liquid. Light is led to the prism at grazing incidence by means of a collimator, and is refracted through the vertical face, the deviation being observed by a telescope rotating about a graduated circle. From this the refractive index is readily calculated if the refractive index of the prism for the light used be known: a fact supplied by the maker. The instrument is also available for determining the refractive index of isotropic solids. A little of the solid is placed in the vessel and a mixture of monobromnaphthalene and acetone (in which the solid must be insoluble) is added, and adjustment made by adding either one or other liquid until the border line appears sharp, i.e. until the liquid has the same index as the solid.
The Herbert Smith refractometer (fig. 7) is especially suitable for determining the refractive index of gems, a constant which is
End of Article: REFRACTION (Lat. refringere, to break open or apart)