(4) To Measure the Wave-Length of Light by means of a Diffraction Grating.

A diffraction grating consists of a number of fine lines ruled at equal distances apart on a plate of glass—a transmission grating; or of speculum metal-a reflexion grating. We will consider the former. If a parallel pencil of homogeneous light fall normally on such a grating, the origin of light being a slit parallel to the lines of the grating, a series of diffracted images of the slit will be seen, and if 0„ be the deviation of the light which forms the nth image, reckoning from the direction of the incident light, d the distance between the centres of two consecutive lines of the grating, and λ the wave-length, we have

The quantity dis generally taken as known, being determined at the time of ruling the grating. The spectrometer is used to determine 0,

The telescope and collimator are adjusted for parallel rays, and the grating placed on the table of the instrument with its lines approximately parallel to the slit. For convenience of adjustment it is best to place it so that its plane is at right angles to the line joining two of the levelling screws. The grating must now be levelled, i.e. adjusted so that its plane is at right angles to the table of the spectrometer. This is done by the method described above for the prism. Then place it with its plane approximately at right angles to the incident light, and examine the diffracted images of the slit. The plane of the grating is at right angles to the line joining two of the levelling screws; the third screw then can be adjusted without altering the angle between the plane of the grating and the table of the spectrometer. Adjust the third screw until the slit appears as distinct as possible; the lines of the grating will then be parallel to the slit.

Turn the table carrying the grating so as to allow the direct light to pass it; adjust the telescope so that the vertical cross-wire bisects the image of the slit seen directly, and read the vernier. This gives us the direct reading. Place the grating with its plane accurately perpendicular to the incident rays, as described above (p. 393), and turn the telescope to view the diffracted images in turn, taking the corresponding readings of the vernier. The difference between these and the direct reading gives us the deviations 01, 02, &c. A series of diffracted images will be formed on each side of the direct rays. Turn the telescope to view the second series, and we get another set of values of the deviation 0', ', &c. If we had made all our adjustments and observations with absolute accuracy, the corresponding values 01, 0'1, &c., would have been the same; as it is their mean will be more accurate than either.

Take the mean and substitute in the formula

We thus obtain a set of values of A.

If the light be not homogeneous, we get, instead of the separate images of the slit, more or less continuous spectra, crossed it may be, as in the case of the solar spectrum, by dark lines, or consisting, if the incandescent body be gas at a low pressure, of a series of bright lines.

In some cases it is most convenient to place the grating so that the light falls on it at a known angle, & say. Let be the angle which the diffracted beam makes with the normal to the grating, and the deviation for the nth image, and being measured on the same side of the normal, then it may be shewn that

and

0 = $ + 4

nλ= d(sin + sin )

=

= d{sin &+sin (0 −6)}.

The case of greatest practical importance is when the deviation is a minimum, and then 40, so that if 0, denote the minimum deviation for the nth diffracted image, we have

λ = 2 d sin 10,

n

In the case of a reflexion grating, if

and denote

the angles between the normal and the incident and reflected now being measured on opposite

rays respectively,

and

sides of the normal, the formula becomes

nλd (sin -sin );

and if be the deviation

0 = π (4+4).

If the value of d be unknown, it may be possible to find it with a microscope of high power and a micrometer eyepiece. A better method is to use the grating to measure 0,, for light of a known wave-length. Then in the formula, nλ = d sin 0,, we know λ, n, and 0, and can therefore determine d.

Experiment.-Determine by means of the given grating the wave-length of the given homogeneous light.

Values of deviations, each the mean of three observations

63. The Optical Bench.

The optical bench (fig. 39) consists essentially of a graduated bar carrying three upright pieces, which can slide. along the bar; the second upright from the right in the

FIG. 39.

figure is an addition to be described later. The uprights are provided with verniers, so that their positions relatively to the bar can be read. To these uprights are attached metal jaws capable of various adjustments; those on the first and second uprights can rotate about a vertical axis through its centre and also about a horizontal axis at right angles to the upright; they can also be raised and lowered.

The second upright is also capable of a transverse motion at right angles to the length of the bar, and the amount of this motion can be read by means of a scale and vernier. The jaws of the first upright generally carry a slit, those of the second are used to hold a bi-prism or apparatus required to form the diffraction bands.

To the third upright is attached a Ramsden's eye-piece in front of which is a vertical cross-wire; and the eye-piece and cross-wire can be moved together across the field by means of a micrometer screw. There is a scale attached to the frame above the eye-piece, by which the amount of displacement can be measured. The whole turns of the screw are read on the scale by means of a pointer attached

T

to the eye-piece. The fractions of a turn are given by the graduations of the micrometer head.

The divisions of the scale are half-millimetres and the micrometer head is divided into 100 parts.

(1) To Measure the Wave-Length of Light by means of Fresnel's Bi-prism.

The following adjustments are required :

(1) The centre of the slit, the centre of the bi-prism, and the centre of the eye-piece should be in one straight line. (2) This line should be parallel to the graduated scale of the bench.

(3) The plane face of the bi-prism should be at right angles to this line.

(4) The plane of motion of the eye-piece should also be at right angles to the same line.

(5) The cross-wire in the eye-piece, the edge of the prism, and the slit should be parallel to each other, and vertical, that is to say, at right angles to the direction of motion of the eye-piece.

To describe the adjustments, we shall begin with (5).

Focus the eye-piece on the cross-wire, and by means of the flat disc to which it is attached, turn the latter round the axis of the eye-piece until it appears to be vertical; in practice the eye is a sufficiently accurate judge of when this is the case.

Draw the third upright some way back, and insert between it and the slit a convex lens. Illuminate the slit by means of a lamp, and move the lens until a real image of the slit is formed in the plane of the cross-wire. Turn the slit round by means of the tangent screw until this image is parallel to the cross-wire. The slit must be held securely and without shake in the jaws.

Move the eye-piece up to the slit and adjust the vertical and micrometer screws until the axis of the eye-piece appears to pass nearly through the centre of the slit, turning at the same time the eye-piece round the vertical axis until its axis appears parallel to the scale. This secures (4) approximately. This is shewn in the figure.