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The B-curve even for 10 will, therefore, deviate but
very little from the central or Cornu-spiral. In other words,
the axial intensity-gradient, for appreciable v, will be very
small (as compared with the transversal one, dI/dp).
Both
curves will start from the origin horizontally. The Cornu
spiral is initially flat while the B-curve has the initial
curvature B=2′′σ/λ, and, if σ<0, an inflexion point for
101
i. e., even for σ|=50λ, very near the origin.
500x'
With the exception of such details the B-curves deviate
but insignificantly from the focal Cornu spiral, and it
would therefore be hardly worth the trouble to draw them
accurately.

v=

London, October 1917,

Research Dept., Adam Hilger, Ltd.

VI. Interferometers for the Experimental Study of Optical
Systems from the point of view of the Wave Theory. By
F. TWYMAN*.

CONTENTS.

1. Description of the Interferometers.
2. Various Uses.

1. Description of the Interferometers.

THESE

HESE instruments in their simplest form resemble the
well-known Michelson interferometer, the main essential
optical difference being that the two interfering beams of
light are brought to a focus at the eye of the observer.

Optical elements or combinations suitable for examination
by means of these instruments may almost all be classed in
two categories. Into the one category fall those combinations
which are required to receive a beam of light which has a
plane wave-front and deliver it again after transmission with
a plane wave-front; and into the other fall those the object
of which is to impart spherical wave-fronts to beams which
are incident on them with plane wave-fronts.
The two corre-
sponding arrangements will be referred to as the prism inter-
ferometer and the lens interferometer respectively.

The Prism Interferometer.

The prism interferometer is shown in diagram (fig. 1) as
arranged for the correction of a 60° prism, such as is used for
spectroscopy.

The light used must consist of monochromatic rays. Such
* Communicated by the Author.
Phil. Mag. S. 6. Vol. 35. No. 205. Jan. 1918.

E

a light may be obtained from a Cooper-Hewett MercuryVapour Lamp, combined with a suitable filter.

The light from the source is reflected by the adjustable mirror A through the condensing-lens B, by means of which it is condensed on the aperture of the diaphragm C.

The diverging beam of light is collimated by a lens D, and falls as a parallel beam on a plane parallel plate K, the second surface of which is silvered lightly so that a part of the

Fig. 1.

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Diagram of Prism Interferometer.

light is transmitted and part reflected. The major part should be reflected. One part passes through the prism L in the same way as in actual use, and being reflected by the mirror F passes back through the prism to the plate K. The other part of the light is reflected to the mirror G and back again to the plate K. Here the separated beams recombine, and passing through the lens E each forms on the eye placed somewhat beyond the aperture in the diaphragm P an image of the hole in the diaphragm C. One of the reflecting mirrors in its mount is shown in fig. 2.

When the mirrors are adjusted, interference-bands are seen which form a contour map to a scale of wave-lengths of the extent to which passage of the beam twice through the prism has distorted the wave-front. This distortion can be Fig. 2.

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Mirror in Mount.

corrected by removing from each point of one prism face, by local polishing, an amount of glass proportional to the distortion of the wave-front at that point; hence it follows that the bands also form a contour map of the glass requiring to be removed in order to make the optical performance of the prism perfect. Fig. 3.

Fig. 3 represents in diagram a typical map, where Q represents the highest point of a "hill." The procedure in such a case is to mark out the contour lines on the surface of the prism with a paint-brush dipped in rouge, and then to

polish first on the region Q, subsequently extending the area of polishing first partly, then wholly, to the next contour line; and so on. The marking out of the prism surface can be done while observing the bands.

Fig. 4.

Fig. 5.

It should be noted that variations in the contour lines are obtained by a tilt of the plane of reference. Thus a slight adjustment of mirror F (fig. 1) might change a contour map

from that shown in fig. 4 to that shown in fig. 5. The form of surface is in each case the same (see the sectional diagrams at the top of the figures), but correction can be carried out according to whichever plane of reference is the most favourable from the point of view of the operator. In order to find whether Q (fig. 3) is a hill or a valley, the cast-iron table M (fig. 1) can be bent with the fingers so as to tilt the mirror F in such a way as to lengthen the ray-path. If the contour line at Qexpands to enclose a larger area, a hill is indicated, and vice versa. Although the words "hill" and "valley" are convenient to use, it must not be supposed that the imperfections necessarily result from want of flatness either of one or of both surfaces of the prism. The contour map gives the total effect on the wave-front produced by double passage through the prism, and shows in wave-lengths the departure from planeness of the resulting wave-surface.

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Diagram of Lens Interferometer.

In the lens interferometer all parts are left as in the prism arrangement except that the mirror F is removed and replaced

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