image of the luminous source. The position of this point can be easily determined. If l be the distance of the source below the surface, l′ the distance of the image, and μ the refractive index, then l′＝l/μ. 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 l above, and between the second and third readings the depth of the image, corresponding to l′.
Refraction by a Prism.—In optics a prism is a piece of transparent 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, Le. 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 μ is found as follows. Let in fig. 2, PQRS be the course of the ray through the prism; the internal angles φ′, ψ′ each equal 12i, and the angles of incidence and emergence φ, ψ are each equal and connected with φ′ by Snell’s law, i.e. sin φ＝μ sin φ′. Also the deviation D is 2 (φ−φ′). Hence μ＝sin φ/sin φ′＝sin12 (D+i)/sin12i.
Fig. 2.
Refractometers.—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 slit 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 determined 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 μ 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 hypotenuse 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
by a lens L. Beneath the prisms is a mirror for reflecting light
Fig. 3.
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
Fig. 4.Fig. 5.
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. In
