are inserted to invert the image. How they do this may be learned from a study of the figure. Since the image produced by L1 is formed at the principal focus of L3, the rays emerging from L are parallel. The second image is formed at the principal focus of L1. When the eye is focused for parallel rays, this second image is at the principal focus of the eyepiece lens, L2. 625. The opera glass. In the opera glass (or Galileo's telescope, as it is sometimes called) a diverging lens (Fig. 429) is used as the eyepiece lens. The converging objective lens L1 would, if the I L1 L2 2 FIG. 429. The opera glass 2 lens L2 were absent, form a real, inverted image at I1. The diverging lens L2, however, bends the rays as shown in the figure; hence, if the eye is placed close to the lens L2, one sees an erect, virtual image, I2. In the figure the image I2 is shown, for convenience, much nearer than it usually is. The virtual image is a great distance away if the eye is focused for parallel rays, as is the case with other forms of telescopes. In focusing for this condition, the lens L2 is moved until the image I1 is at the principal focus of the lens L2. The opera glass has a relatively small field of view and is suitable for only small magnifications. Even large-sized field glasses of this type magnify only from three to six times. Their chief advantage is that they are shorter than the telescopes described above. 626. The prism binocular. The best field glasses for giving good magnifying power and relatively large fields of view are the prism binoculars. In Fig. 430 is shown the ray path. This type is essentially an astronomical telescope with the inversion produced by reflection inside totally reflecting prisms. The rays, after passing through the objective lens L1, are totally reflected back by the prism A to the prism B. This prism reflects the rays through the eyepiece lens L2. The length of the optical path is nearly three times the length of the instrument, and permits the use of an objective with longer focal length, thus giving greater magnification. The images are formed in the same relative positions as in the case of the astronomical telescope. If the eye is focused for parallel rays, the image produced by the objective L1 is at the the top and bottom. Hence the image is seen in its proper position. The term binocular arises from the fact that the telescopes are mounted in pairs, one for each eye. 627. The reflecting telescope. In the reflecting telescope a concave mirror is used to form a real image of the object. This image is viewed with an eyepiece lens as in the case of the astronomical telescope. Inasmuch as the light is reflected back, special arrangements must be made so that the observer does not obstruct the incoming light. In one method the mirror is tipped a little, and the reflected beam then forms the image off at one side; in another a small plane mirror or a reflecting prism is placed directly in front of the mirror and reflects the converging rays off to one side. Very large reflecting telescopes have been constructed for astronomical purposes. A number have been built which are much larger than any refracting telescope. There is one at the Mt. Wilson Solar Observatory (near Pasadena, California) having a concave mirror 100 inches across. The largest lens in use is the objective in the large telescope of the Yerkes Observatory at Williams Bay, Wisconsin. This is 40 inches in diameter. 628. The range-finder. In Fig. 431 is shown the plan of one of the best types of range-finder. At a fixed distance apart are mounted two totally reflecting prisms of the type called penta prisms. In this type the two reflecting surfaces are at an angle of 45 degrees with each other, and the reflected ray always makes an angle of 90 degrees with the incident one, no matter what the direction of the incident ray may be, provided the ray enters and leaves the two faces which are at right angles to each other. This type of prism is sometimes called a constant-deviation-reflecting prism. Near each of the penta prisms B and D are the lenses L1. Each of these lenses, together with the reflecting prism M or N and the eyepiece lens L2, forms a telescope. The reflecting prisms M and N are placed one above the other; hence to one looking through the eyepiece lens the upper half of the field of view is seen by means of the light coming through the prism D, and the lower half by means of the light coming through the prism B. If the object viewed is at such a great distance that the rays A and Care parallel, and the reflecting faces of M and N are at right angles, the two halves of the field of view will match, and one continuous image will be seen. But since the two prisms M and N are not set exactly at right angles, a thin wedge of glass must be placed at W1 to bend the rays so that the two halves of the field will match. If, now, a nearer object is looked at, the light rays from it will not be parallel, but will have the directions of the lines A and E. The ray leaving D will be bent downward, as shown by the broken line in the figure. In order to make the two halves match, the thin wedge must be moved to the position W2. In a similar manner it can be shown that for different distances of the object the wedge must be moved to different positions. The instrument is so constructed that the motion of the wedge moves an index along a calibrated scale, from which distances of the object can be read off directly. For example, when the wedge is at W1, the scale should read infinity; when it is moved a little, 10,000 yards; when it is in a position much nearer W2, 1000 yards. PROBLEMS 1. A photographic camera has a focal length of 6 in. How much farther from the lens is the image of an object 10 ft. away than that of an object 100 ft. away? 2. The picture on a lantern slide is 24×3+ in. What should be the focal length of a projection lens in order to make the picture on the screen 7×10 ft.? (The screen is 30 ft. from the lens.) 3. The projection lens of a lantern has a focal length of 8 in. When the screen is 20 ft. from the lens, what will be the magnification of a slide ? 4. If the distance of most distinct vision is 25 cm., what is the magnifying power of a converging lens with a focal length of 3 cm., when the lens is used as a simple microscope ? 5. In a compound microscope the image formed by the objective lens, focal length 5 mm., is 20 cm. from the lens. The eyepiece lens produces a magnification of 10. Find the total magnification. 6. A compound microscope has an objective with a focal length of 4 mm., and an eyepiece lens with a focal length of 4 cm. The real image produced by the objective is 20 cm. from the objective. The final image is 25 cm. from the eyepiece lens. Compute the magnification. 7. A microscope having an objective lens with a focal length of half an inch is used to form an image of a slide upon a screen which is 20 ft. from the lens. What is the magnification? 8. The objective lens of an astronomical telescope has a focal length of 6 ft., and the eyepiece lens a focal length of 2 in. Compute the magnification that the telescope will produce when used for viewing distant objects. 9. The objective of an astronomical telescope has a focal length of 120 in., and the eyepiece lens a focal length of 2 in. While viewing a fardistant object the distance between the lenses was 121 in. (a) Where was the image that the eye saw? (b) Was the image real or virtual, erect or inverted? 10. The objectives of a pair of binoculars have focal lengths of 10 in. How much farther from the objective lenses are the images of an object 20 ft. away than those of an object very far away? 1 CHAPTER XLV SPECTRA AND COLOR PHENΟΜΕΝΑ Pure spectra, 629. Types of spectra, 630. Emission spectra, 631. Absorption spectra, 632. Summary of types of spectra, 633. Luminescence, 634. Some applications of spectrum analysis, 635. The Doppler effect, 636. The complete spectrum, 637. Methods of detecting ultra-violet and infrared radiations, 638. The rainbow, 639. Coronas; halos, 640. The color of a body, 641. The mixing of colors, 642. Complementary colors, 643. The mixing of pigments, 644. Fluorescence; phosphorescence, 645. 629. Pure spectra. Newton showed by a method explained in section 598 that white light is a mixture of different kinds of light -kinds which produce different colors. It is frequently a matter of importance, not only in work in physical science but in many other cases, to be able to break up a beam of light into its component parts. The simplest method is to produce a spectrum by refraction through a prism. In doing this, one needs to employ certain precautions; otherwise he will not get a pure spectrum but will get, at each point in the spectrum, mixtures of different colors. In a pure spectrum there must be no appreciable overlapping of colors; that is, the light which reaches a given narrow region of the spectrum must be light of only one kind. In the production of a pure spectrum a narrow source of light is absolutely necessary (the reason for this will appear later). In Fig. 432, S is a narrow slit, the length of the slit being perpendicular to the plane of the figure. As far as the focusing is concerned, the slit is the source of light. Let us suppose that the source emits only one kind of light, say blue light. When the lens L is placed so that the image of the slit will be at S', the prism P placed in the path of the light will cause the image to be formed at S1. In this case there will be no breaking up of the beam of light by the prism, for light of only one frequency is |