Also since DC and C Q' are the directions of the same ray inside and outside respectively,

COS O CAμ COS D C A;

..sin(p+D)= μ sin(p' + 2 );

.. sin &+D cos & = μ (sin &' + 2 i cos ☀'),

Again, it may happen that one or both faces of the piece of glass are curved; it will then act as a lens, and the following method will give its focal length. The method may be advantageously used for finding the focal length of any long-focussed lens.

Direct the telescope to view the collimator slit, and focus it; interpose the lens in front of the object-glass. The focus of the telescope will require altering to bring the slit distinctly into view again.

Let us suppose that it requires to be pushed in a distance x. Let be the distance between the lens and the objectglass of the telescope, then the parallel rays from the collimator would be brought to a focus at a distance ƒ behind the lens, i.e. at a distance f-c behind the object-glass; they fall, however, on the object-glass, and are brought by it to a focus at a point distant F-x from the glass.

If the lens be concave, the eye-piece of the telescope will require pulling out a distance x suppose; and in this case the rays falling on the object-glass will be diverging from a point at a distance f+c in front of it, and will converge to a point at a distance F+x behind it.

We infer, then, that if the eye-piece requires pushing in the lens is convex, and if it requires pulling out it is

concave.

Moreover, we note that all the above formulæ both for reflexion and refraction are simplified if F = c; that is to say, if the distance between the object-glass and the reflecting surface or lens, as the case may be, is equal to the focal length of the object-glass.

If this adjustment be made, and if x be the displacement of the eye-piece in either case, we have for the radius of curvature of the surface

(1) Measure the curvature of the faces of the given piece of glass.

(2) If both faces are plane, measure the angle between

them.

(3) If either face is curved, measure the focal length of the lens formed by the glass.

Enter results thus:

(1) Scale used divided to fiftieths of an inch. Angle of incidence 45°.

SPECTRA, REFRACTIVE INDICES, AND WAVE-LENGTHS. A BEAM of light generally consists of a combination of differently-coloured sets of rays; the result of the decomposition of a compound beam into its constituents is called. a spectrum. If the beam be derived from an illuminated aperture, and the spectrum consist of a series of distinct images of the aperture, one for each constituent set of rays of the compound light, the spectrum is said to be pure. A spectroscope is generally employed to obtain a pure Spectrum. The following method of projecting a pure

spectrum upon a screen by means of a slit, lens, and prism, illustrates the optical principles involved.

The apparatus is arranged in the following manner.

The lamp is placed at L, fig. 34, with its flame edgewise to the slit; then the slit s and the lens м are so adjusted as to give a distinct image of the slit at s' on the screen A B; the length of the slit should be set vertical. The prism P Q R is then placed with its edge vertical to receive the rays after passing through the lens. All the rays from the lens should

fall on the front face of the prism, which should be as near to the lens as is consistent with this condition. The rays will be refracted by the prism, and will form a spectrum A' B' at about the same distance from the prism as the direct image s'. Move the screen to receive this spectrum, keeping it at the same distance from the prism as before, and turn the prism about until the spectrum formed is as near as possible to the position of s', the original image of the slit; that is, until the deviation is a minimum. The spectrum thus formed is a pure one, since it contains an image

of the slit for every different kind of light contained in the incident beam.

60. The Spectroscope.

Mapping a Spectrum.

We shall suppose the spectroscope has more than one prism.

Turn the telescope to view some distant object through an open window, and focus it. In doing this adjust first the eye-piece until the cross-wires are seen distinctly, then move the eye-piece and cross-wires by means of the screw until the distant object is clear. The instrument should be focussed so that on moving the eye about in front of the eye-lens no displacement of the image relatively to the cross-wires can be seen.

Remove the prisms, and if possible turn the telescope to look directly into the collimator. Illuminate the slit and focus the collimator until the slit is seen distinctly. Replace one prism and turn the telescope so as to receive the refracted beam. Turn the prism round an axis parallel to its edge until the deviation of some fixed line is a minimum (see § 62, p. 391).

For this adjustment we can use a Bunsen burner with a sodium flame.

If the prism have levelling screws, adjust these until the prism is level.

To test when this is the case fix a hair across the slit, adjusting it so that when viewed directly it may coincide with the horizontal cross-wire of the eye-piece. The hair will be seen in the refracted image cutting the spectrum horizontally. Adjust the levelling screws of the prism until this line of section coincides with the cross-wire.

In some instruments the prisms have no adjusting screws, but their bases are ground by the maker so as to be at right angles to the edge.

Having placed the first prism in position, secure it there