891 a. Prism Binoculars.-Field glasses which combine high magnifying power and large field of view are now made according to the plan shown in figure 552.

The beam of light from the object-glass enters a right-angled glass prism and after two internal reflections, at A and B, is completely reversed in direction and travels back to a second prism, placed at right angles to the first, where it is again totally reflected, at C and D, and turned back again toward the eye lens E.

The reflections in the two prisms secure an erect image without using the reversing lenses of the ordinary terrestrial tele

B

FIG. 552.-Path of rays in prism binocular.

scope; for one prism interchanges the two sides of the image, while the other makes it upright, thus restoring it completely to its natural position.

Also, on account of the length of the path of the rays from the object glass to the eye lens, the focal length of the object glass may be three times as great as in the ordinary field glass, and the magnifying power correspondingly increased.

892. Reflecting Telescopes.-Instead of the object-glass of a telescope, a long-focus concave mirror may be used. The arrangement shown in figure 553 was used in Sir William Hershel's great telescope, the mirror M being slightly inclined so that the eye-piece and the observer's head were not in the line of the rays falling in the mirror. In small reflecting telescopes the rays converging toward the image I may be reflected out sideways to the eye-piece by a small mirror placed directly in front of the large mirror, as was done by Newton. To obtain a perfect image free from spherical aberration the mirror must be parabolic instead of spherical. A mirror has the advantage of form

ing an image free from chromatic aberration since all wave lengths of light are reflected alike.

A telescope mirror is called a speculum, and may be made of an alloy called speculum metal which takes a fine polish and does not readily tarnish. Specula are now, however, usually made of glass, as this is harder and less dense than speculum metal. The surface is ground and polished to the required shape and then silvered.

1. A plano-convex lens, in which the convex side has a radius of curvature of 1 meter, is made of glass such that its index of refraction for red is 1.53 while for short waves in the blue it is 1.55; find how much farther from the lens the principal focus for red is than for blue.

2. In a projection apparatus it is desired that the pictures shall be 10 ft. wide on a screen 40 ft. distant when the slides are 3 in. wide. What must be the focal length of the projecting lens used? 3. By means of a microscope objective, a scale having 50 lines to the millimeter is projected upon a screen 9 meters distant, and the distance between the lines in the image on the screen is 4 cm. What is the focal length of the objective used?

4. Make a graphic construction, tracing through a simple astronomical telescope a pencil of three oblique rays which come parallel among themselves from a distant object and meet the object-glass at the top, middle, and bottom, respectively. The lenses may be made 4 cm. in diameter, with focal lengths 54 and 6 cm., and 60 cm. apart. Take the incident pencil as oblique as possible and yet so that all the rays pass through the instrument. Indicate also the position of the eye.

5. Make a similar construction in case of Galileo's form of telescope, the focal lengths being the same as in Problem 4, but the distance between the lenses being 47 cm. Draw in this case two oblique pencils of three rays each, one coming from the top of the distant object and one from the bottom. Show where the eye must be placed to see as much as possible.

6. Make a construction of an astronomical telescope as in Problem 4 and then add two convergent lenses of 4 cm. focal length each, so as to erect the image as shown in figure 551. One lens is to be put just far enough back of the eye lens of the telescope so that the pencil of rays through the bottom of one will be transmitted through the top of the other. The other must be placed to make the emergent pencil parallel. Mark the eye-spot.

ANALYSIS OF Light.

The Spectrum

893. The Spectrum.-It has been seen that when light passes through a prism it is spread out in a colored band shading from red to violet and called the spectrum, showing that a beam of white light is complex and made up of different kinds of light which are separated by the prism in consequence of their different refrangibilities. These lights also differ in the color sensations which they excite, the least refrangible being the red rays while the most refrangible are the violet.

It will be shown later that the physical property which determines the refrangibility of a ray of light is wave length; so that in forming a spectrum we are really spreading out the light in the order of wave lengths, the longest waves being at the red end of the spectrum and the shortest at the violet.

894. Pure Spectrum. To obtain a complete analysis of light there must be no overlapping of different kinds, but each must be separated by the prism from every other. To accomplish this the following arrangement may be employed.

The light to be examined enters through a narrow slit S, which is parallel to the edge of the prism and therefore perpendicular to the plane of the paper in the diagram. A converging lens L is so placed that it would bring the light to focus and form at S' an image of the slit if the prism were not interposed.

By the action of the prism, however, the light is refracted downward and if there were only one kind of light present the whole beam would be equally refracted and the bright image of the slit would be formed at R, say, instead of at S', but without any change in color. If, however, there were in the original beam two kinds of light which were differently refracted, then there would be formed two images of the slit, one at R and one

P

-S'

FIG. 554.

at B. And since light waves that are refracted differently also act differently upon the eye, the images at R and B will be of different colors. But if the original beam contained waves of every conceivable degree of refrangibility within certain limits, there would be an infinite number of images of the slit with no separation between them and even overlapping, producing a continuous band of color, shading from one extreme to the other. When the slit is narrow so that the amount of overlapping is small the spectrum is said to be pure.

FIG. 555.-Fraunhofer lines. The wave lengths are given in millionths of a millimeter.

895. Fraunhofer Lines. When the sun spectrum is formed as above described, using a narrow slit so as to produce a pure spectrum, a large number of dark lines are observed which cross the spectrum parallel to the slit, showing that sunlight does not contain all kinds of light, but that certain wave lengths are

lacking, and consequently no bright images of the slit are formed at the corresponding points of the spectrum. These dark lines characteristic of sunlight were first carefully studied by Fraunhofer and are known as the Fraunhofer lines. Some of the most prominent of them are designated by letters of the alphabet, and they furnish convenient points of reference in the spectrum, the A line being almost at the limit of visibility in the red while the H line is near the extreme violet.

896. Analysis of Light by Spectroscope. For the more exact analysis of the light from any source a spectroscope is used. The main features of this instrument are indicated in figure 556.

Light from the source to be studied enters the narrow slit S at the focus of the collimating lens, diverges through that lens and then passes as a parallel beam to the prism P where it is refracted and dispersed. After passing the prism the beam enters the telescope and forms a sharply defined spectrum at the principal focus of the object-glass of the telescope, a separate image of the slit being formed by each wave length of light present. This spectrum is magnified by the eye-piece of the telescope.

An illuminated scale is also sometimes mounted so that light from the scale, reflected at the second face of the prism, enters the telescope and forms an image of the scale along with the spectrum at RV. The observer can by this means locate a definite line in the spectrum by its position on the scale.

To compare the spectra from two separate sources a com