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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 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.
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 Fresnell's Bi-prism.
The following adjustments are required:
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.
Draw the eye-piece away from the slit, say 20 or 30 cm. off, and place the bi-prism in position, turning it about until its plane face appears to be at right angles to the scale of the bench. This secures (3) approximately.
Look through the eye-piece. A blurred image of Fresnel's bands may probably be visible. By means of the traversing screw move the second upright at right angles to the scale until this image occupies the centre of the field. If the bands be not visible, continue to move the screw until they come into the field.
It may be necessary to alter the height of the bi-prism by means of the vertical adjustment so that its centre may be at about the same level as those of the slit and eye-piece.
By means of the tangent screw turn the bi-prism round the horizontal axis at right angles to its own plane until the lines appear bright and sharp.
Adjustment (5) is then complete.
Now draw the eye-piece back along the scale; if the lines still remain in the centre of the field of view, it follows that the slit, the centre of the bi-prism, and the centre of the eye-piece are in one straight line parallel to the scale.
If this be not the case, alter the position of the eye-piece by means of the micrometer screw and that of the bi-prism by means of the traversing screw with which the second stand is furnished, until the lines are seen in the centre of the field for all positions of the eye-piece along the scale bar of the instrument.
Adjustments (1) and (2) have thus been effected.
For (3) and (4) it is generally sufficient to adjust by eye, as already described. If greater accuracy be required, the following method will secure it.
Move the lamp to one side of the slit and arrange a small mirror so as to reflect the light through the slit and along the axis of the instrument. The mirror must only cover one-half of the slit, which will have to be opened somewhat widely. Place your eye so as to look through the other half of the slit in the same direction as the light. Images of the slit reflected from the faces of the bi-prism and probably from other parts of the apparatus will be seen.
Suppose the flat face of the bi-prism is towards the slit. Turn the prism round a vertical axis until the image reflected at the flat face appears directly behind the centre-line of the bi-prism, then clearly the plane of the bi-prism is at right angles to the incident light, and that is parallel to the scale
In making the adjustment, the stand holding the prism should be placed as far as may be from the slit.
If the bevelled face be towards the slit, two images will be seen, and these must be adjusted symmetrically one on each side of the centre.
To adjust the eye-piece employ the same method, using the image reflected from the front lens or from one of the brass plates which are parallel to it. To do this it may be necessary to remove the bi-prism - if this be the case, the eye-piece adjustment must be made first.
As soon as the adjustments are made the various moving pieces must be clamped securely.
It is necessary for many purposes to know the distance between the slit and the cross-wire or focal plane of the eyepiece. The graduations along the bar of the instrument will not give us this directly; for we require, in addition, the horizontal distance between the zero of the vernier and the slit or cross-wire respectively.
To allow for these, take a rod of known length, a centimetres suppose; place one end in contact with the slit, and bring up the eye-piece stand until the other end is in the focal plane. Read the distance as given by the scale between the slit and eye-piece uprights; let it be b centimetres.
Then clearly the correction a-b centimetres must be added to any scale reading to give the distance between the slit and the eye-piece. This correction should be determined before the bi-prism is finally placed in position.
To use the bi-prism to measure λ, the wave-length of light, we require to know c, the distance between the virtual images formed by the bi-prism, x the distance between consecutive bright bands, and a the distance between slit and eye-piece.(1)
Then we have
The distance x is measured by means of the micrometer attached to the eye-piece.
In order that x may be large, c should be small and a large. This is attained by making the distance between the slit and the prism small, 10 to 20 cm., and that between the prism and the eye-piece considerable. Of course the bands are fainter and less distinct if this distance be very large; it must therefore not exceed a certain limit, which depends greatly on the source of light used.
Suppose we have a Bunsen burner with a sodium bead in it.
In making the measurement of x, the micrometer screw of the eye-piece should be always turned in the same direction. This avoids the error of 'lost time' due to any shake in the screw or looseness between the screw and the nut.
Turn the screw to carry the cross-wire as near to one edge of the field as is convenient and set it on the centre of a bright band. Read the scale and micrometer; let the reading be 10.35. Turn the screw until the wire is over the next bright band and read again; let the reading be 10.72. Proceed thus across the field, reading the position of every bright line, and taking an even number, say ten or twelve readings.
Let them be
(1) 10.35 (6) 12.15 (2) 10.72 (7) 12.53 (3) 11.07 (8) 12.88 (4) 11.45 (9) 13.24 (5) 11.81 (10)13.59
Subtract the first from the sixth, the second from the seventh, and so on. Then
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. Thus
x = 0.359 mm.
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 shown 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 be c1 and c2 then it is easy(2) to show that c = sqrt(c1c2).
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 image by reflexion at a large angle of incidence from a plane glass surface (Lloyd's Experiment).
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 c, then x = bλ/c,
where b 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.
Enter results thus: -
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