Subtract the first from the sixth, the second from the seventh, and so on.

Each of these differences is the space covered by a group of six bright lines. Take the mean. We have 1'798. Dividing by five we get the mean value for x.

x=359 mm.

Thus

To determine a we have only to read the verniers at the slit and eye-piece respectively, take the difference and correct it as already described for index error.

To determine c, draw the eye-piece away to about 50 centimetres from the slit and insert between the prism and the eye-piece a convex lens.

It is convenient to have a fourth sliding upright arranged to carry this, as is shewn in the figure.

Two positions for this lens can in general be found, in each of which it will form in the focal plane of the eyepiece distinct images of the two virtual images of the slit.

The distance between these two images in each of these two positions respectively can be found by means of the micrometer screw. Let them bec, and c, then it is easy1 to shew that c = √/c2 €2.

We may replace the bi-prism by Fresnel's original apparatus of two mirrors, arranging the bench so as to give the fundamental interference experiment

Or, again, instead of two mirrors, we may obtain interference between the light coming from the slit and its

I See Glazebrook, Physical Optics, p. 118.

image by reflexion at a large angle of incidence from a plane glass surface (Lloyd's Experiment).

Diffraction Experiments.

The apparatus may be used to examine the effects of diffraction by various forms of aperture.

The plate with the aperture is placed in the second upright in the place of the bi-prism.

If we have a single edge at a distance a from the slit, and if b be the distance between the edge and the eye-piece, x the distance between two bright lines

If the obstacle be a fibre of breadth, then x =

όλ

where is distance between the fibre and the screen or eye-piece.

This formula, with a knowledge of the wave-length of the light, may be used to measure the breadth of the fibre. (Young's Eriometer.)

In order to obtain satisfactory results from diffraction experiments a very bright beam of light is required. It is best to use sunlight if possible, keeping the beam directed upon the slit of the optical bench by means of a heliostat.

Experiments.-Measure the wave-length of light by means of the bi-prism.

405

CHAPTER XV.

POLARISED LIGHT.

On the Determination of the Position of the Plane of

Polarisation.1

THE most important experiments to be made with polarised light consist in determining the position of the plane of polarisation, or in measuring the angle through which that plane has been turned by the passage of the light through a column of active substance, such as a solution of sugar, turpentine, or various essential oils, or a piece of quartz.

The simplest method of making this measurement is by the use of a Nicol's or other polarising prism. This is mounted in a cylindrical tube which is capable of rotation about its own axis. A graduated circle is fixed with its centre in the axis of the tube, and its plane at right angles to the axis, and a vernier is attached to the tube and rotates with it, so that the position, with reference to the circle, of a fiducial mark on the tube can be found. In some cases the vernier is fixed and the circle turns with the Nicol. If we require to find the position of the plane. of polarisation of the incident light, we must, of course, know the position of the principal plane of the Nicol relatively to the circle. If we only wish to measure a rotation a knowledge of the position of this plane is unnecessary, for the angle turned through by the Nicol is, if our adjustments be right, the angle turned through by the plane of polarisation.

For accurate work two adjustments are necessary :— (1) All the rays which pass through the Nicol should be parallel.

(2) The axis of rotation of the Nicol should be parallel to the incident light.

To secure the first, the source of light should be small;

1 See Glazebrook, Physical Optics, chap. xiv.

in many cases a brightly illuminated slit is the best. It should be placed at the principal focus of a convex lens ; the beam emerging from the lens will then consist of parallel rays.

To make the second adjustment we may generally consider the plane ends of the tube which holds the Nicol as perpendicular to the axis of rotation. Place a plate of glass against one of these ends and secure it in this position. with soft wax or cement. The incident beam falling on this plate is reflected by it. Place the plate so that this beam after reflexion retraces its path. This is not a difficult matter; if, however, special accuracy is required, cover the lens from which the rays emerge with a piece of paper with a small hole in it, placing the hole as nearly as may be over the centre of the lens. The light coming through the hole is reflected by the plate, and a spot of light is seen on the paper. Turn the Nicol about until this spot coincides with the hole; then the incident light is evidently normal to the plate-that is, it is parallel to the axis of rotation of the Nicol.

If still greater accuracy be required, the plate of glass may be dispensed with, and a reflexion obtained from the front face of the Nicol. This, of course, is not usually normal to the axis, and hence the reflected spot will never coincide with the hole, but as the Nicol is turned, it will describe a curve on the screen through which the hole is pierced. If the axis of rotation have its proper position and be parallel to the direction of the incident light, this curve will be a circle with the hole as centre. The Nicol then must be adjusted until the locus of the spot is a circle with the hole as centre.

When these adjustments are completed, if the incident light be plane-polarised, and the Nicol turned until there is no emergent beam, the plane of polarisation is parallel to the principal plane of the Nicol; and if the plane of polarisation be rotated and the Nicol turned again till the emergent beam is quenched, the angle turned through by

the Nicol measures the angle through which the plane of polarisation has been rotated.

But it is difficult to determine with accuracy the position of the Nicol for which the emergent beam is quenched. Even when the sun is used as a source of light, if the Nicol be placed in what appears to be the position of total extinction, it may be turned through a considerable angle without causing the light to reappear. The best results are obtained by using a very bright narrow line of light as the source-the filament of an incandescence lamp has been successfully employed by Mr. McConnel-as the Nicol is turned, a shadow will be seen to move across this line from one end to the other, and the darkest portion of the shadow can be brought with considerable accuracy across the centre of the bright line. Still, for many purposes, white light cannot be used, and it is not easy to secure a homogeneous light of sufficient brightness. Two principal methods have been devised to overcome the difficulty; the one depends on the rotational properties of a plate of quartz cut normally to its axis; the other, on the fact that it is comparatively easy to determine when two objects placed side by side are equally illuminated if the illumination be only faint. We proceed to describe the two methods.

64. The Bi-quartz.

If a plane-polarised beam of white light fall on a plate of quartz cut at right angles to its axis, it has, as we have said, its plane of polarisation rotated by the quartz. But, in addition to this, it is found that the rays of different wavelengths have their planes of polarisation rotated through. different angles. The rotation varies approximately inversely as the square of the wave-length; and hence, if the quartz be viewed through another Nicol's prism, the proportion of light which can traverse this second Nicol in any position will be different for different colours, and the quartz will appear coloured. Moreover, the colour will vary as the