61. Measurement of the Index of Refraction of a Plate by means of a Microscope.

Let p (fig. 37) be a point in a medium of refractive index and let a small pencil of rays diverging from this point fall directly on the plane-bounding surface of the medium and emerge into air.

FIG. 37

Let A be the point at which the axis of the pencil emerges, and Q a point on PA, such that AP=μAQ; then the emergent pencil will appear to diverge from Q, and if we can measure the distances AP and AQ we can find μ To do this, suppose we have a portion of a transparent medium in the form of a plate, and a microscope, the sliding tube of which is fitted with a scale and vernier or at least a pointer, so that any alteration in the position of the object-glass when the microscope is adjusted to view objects at different distances may be measured.

P

Place under the object-glass a polished disc of metal with a fine cross engraved on it, and bringing the cross into the centre of the field, focus the microscope to view and read the scale. Repeat the observation several times, taking the mean. Now bring between the metal plate and the object-glass the transparent plate, which, of course, must not be of more than a certain thickness. One surface of the plate is in contact with the scratch on the metal, which thus corresponds to the point P; the emergent rays therefore diverge from the point Q, and in order that the scratch may be seen distinctly through the plate, the microscope will require to be raised until its object-glass is the same distance from Q as it was originally from P. Hence, if we again focus the microscope to see the cross, this time through the plate, and read the scale, the difference between the two readings

will give us the distance P Q Let us call this distance a, and let t be the thickness of the plate, which we can measure by some of the ordinary measuring apparatus, or, if more convenient, by screwing the microscope out until a mark, made for the purpose, on the upper surface of the plate comes into focus, and reading the scale on the tube. We thus can find PA = t, PQ = a

A modification of this method is useful for finding the index of refraction of a liquid.

Suppose the liquid to be contained in a vessel with a fine mark on the bottom.

Focus on the mark through the liquid, and then on a grain of lycopodium dust floating on the surface. If the depth be d1, the difference between the readings gives us du; let us call this difference a. Then

Now add some more liquid until the depth is d1 +d2. Focus on the mark again, and then a second time on the floating lycopodium which has risen with the surface; let the difference between these two be b; then

d1 + d2 b =

μ

But the difference between the second and fourth reading, that is to say, of the two readings for the lycopodium grains is clearly the depth of liquid added, so that from these two readings d is obtained, and we have

Experiment.-Determine the index of refraction (1) of the given plate and (2) of the given liquid.

Enter results thus:

This instrument (fig. 38) consists of a graduated circle, generally fixed in a horizontal position. A collimator is rigidly attached to the circle. The axis of the collimator is in a plane parallel to that of the circle, and is directed to a point vertically above the centre of the circle. A movable arm, FIG. 38.

fitted with a clamp and tangent screw, carries an astronomical telescope which is generally provided with a Ramsden's eye-piece and cross-wires. The position of the telescope with reference to the circle is read by means of a vernier.' Above the centre of the circle there is a horizontal table, which is generally capable of rotation about the vertical axis of the I See Frontispiece, figs. 5 and 6.

C C

circle; and this table has a vernier attached to it, so that its position can be determined. The whole instrument rests on levelling screws, and the telescope and collimator are held in their positions by movable screws, so that their axes can be adjusted till they are parallel to the circle.

On the Adjustment of a Spectrometer.

The line of collimation, or axes of the telescope and collimator should lie in one plane, and be always perpendicular to the axis about which the telescope rotates. To secure absolute accuracy in this is a complicated problem.

In practice it is usually sufficient to assume that the axes of the telescope and collimator are parallel to the cylindrical tubes which carry the lenses. Level the table of the instrument by means of a spirit-level and the levelling screws, afterwards level separately the telescope and collimator by means of a level and the set screws attached to each. The axis of each is now parallel to the plane of the circle. See that the clamp and tangent screw work properly, and that the instrument is so placed that the vernier can be read in all positions in which it is likely to be required.

Focus the eye-piece of the telescope on the cross-wires or needle-point. Turn the telescope to some very distant object, and focus the object-glass by the parallel method described on p. 369. Turn the telescope to look into the collimator; illuminate the slit, and then focus it by altering its position with reference to the lens of the collimator. When the slit is in focus, the light issuing from the collimator forms a series of pencils of parallel rays.'

This is a very important adjustment; if it be properly carried out the direction of the rays forming an image after reflexion or refraction at the surface of a prism, and hence the circle readings, will be the same, no matter to what extent the prism may be moved parallel to itself about the spectrometer table. In the absence of such an adjustment the measurements would require a prism with indefinitely small width of face and its edge coincident with the axis of rotation. It will be seen that the faces of a prism for accurate optical work must be plane. A prism which shews by the alteration of focus which it produces that its faces are not plane must be discarded except for roughly approximate measurements.

In experiments in which a prism is used it is generally necessary that the edge of the prism should be parallel to the axis of rotation of the telescope. Turn the telescope to view the slit directly. Fix by means of soft wax a hair or silk fibre across the slit, so that it may appear to coincide with the horizontal cross-wire or point of the needle when seen through the instrument; or, as is often more convenient, cover up part of the slit, making the junction of the covered and uncovered portions coincide with the horizontal wire. Fix the prism with wax or cement on to the levelling table in the centre of the instrument, so that the light from the collimator is reflected from two of its faces, and adjust it by hand, so that the two reflected images of the slit can be brought in turn into the field of view of the telescope. Alter the set screws of the levelling table until the image of the hair across the slit when reflected from either of the two faces, and seen through the telescope, coincides with the intersection of the cross-wires. When this is the case the prism is in the required position.

The edge of the prism may also be adjusted to be parallel to the axis of rotation by setting the two faces successively at right angles to the line of collimation of the telescope. This may be done with great accuracy by the following optical method. Illuminate the cross-wires of the telescope, and adjust the face of the prism so that a reflected image of the cross-wires is seen in the field of view of the telescope coincident with the wires themselves. This can only be the case when the pencil of light from the intersection of the wires is rendered parallel by refraction at the object-glass of the telescope, and reflected normally by the face of the prism, so that each ray returns along its own path (see § P). An aperture is provided in the eye-piece tubes of some instruments for the purpose of illuminating the wires; in the absence of any such provision, a piece of plane glass, placed at a suitable angle in front of the eyepiece, may be used. It is sometimes difficult to catch sight