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The relation shows that in order to get a high magnifying power with a compound microscope the focal length of both eyepiece and objective should be as short as possible, while the tube length should be as long as possible. Thus, if a microscope has both an eyepiece and an objective of 6 millimeters focal length and a tube 15 centimeters long, its magni25 × 15 fying power will be

1042. Magnifications as high as 2500 or

.6 x .6 3000 are sometimes used, but it is impossible to go much farther, for the reason that the image becomes too faint to be seen when it is spread over so large an area.

459. The opera glass. On account of the large number of lenses which must be used in the terrestrial telescope, it is too bulky and awkward for many purposes, and hence it is often replaced by the opera glass (Fig. 435). This instrument consists of an objective like that of

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FIG. 435. The opera glass

the telescope, and an eyepiece which is a concave lens of the same focal length as the eye of the observer. The effect of the eyepiece is therefore to just neutralize the lens of the eye. Hence the objective, in effect, forms its image directly upon the retina. It will be seen that the size of the image formed upon the retina by the objective of the opera glass is as much greater than the size of the image formed by the naked eye as the focal length CR of the objective is greater than the focal length CR of the eye. Since the focal length of the eye is the same as that of the eyepiece, the magnifying power of the opera glass, like that of the astronomical telescope, is the ratio of the focal lengths of the objective and eyepiece. Objects seen with an opera glass appear erect, since the image formed on the retina is inverted, as is the case with images formed by the lens of the eye unaided.

460. The stereoscope. Binocular vision. When an object is seen with both eyes, the images formed on the two retinas differ slightly, because of the fact that the two eyes, on account of their lateral separation, are viewing the object from slightly different angles. It is this difference

in the two images which gives to an object or landscape viewed with two eyes an appearance of depth, or solidity, which is wholly wanting when one eye is closed. The stereoscope is an instrument which reproduces in photographs this effect of binocular vision. Two photographs of the same object are taken from slightly different points of view. These photographs are mounted at A. and B (Fig. 436), where they are simultaneously viewed by the two eyes through the two prismatic lenses m and n. These two lenses superpose the two images at C because of their action as prisms, and at the same time magnify them because of their action as simple magnifying lenses. The result is that the observer is conscious of viewing but one photograph; but this differs from ordinary photographs in that, instead of being flat, it has all of the characteristics of an object actually seen with both eyes.

The opera glass has the advantage over the terrestrial telescope of affording the benefit of binocular vision; for while telescopes are usually constructed with one tube, opera glasses always have two, one for each eye.

461. The Zeiss binocular. The greatest disadvantage of the opera glass is that the field of view is very small. The terrestrial telescope has a larger field but is of inconvenient length. An instrument called the Zeiss binocular (Fig. 437) has recently come into use, which combines the compactness of the opera glass with the wide field of view of the terrestrial telescope. The compactness is gained by causing the light to pass back and forth through total reflecting prisms, as in the figure. These reflections also perform the function of reinverting the image, so that the real image which is formed at the focus of the eyepiece is erect. It will be seen, therefore, that the instrument is essentially an astronomical telescope in which the image is reinverted by reflection, and in which the tube is shortened by letting the light pass back and forth between the prisms.


FIG. 436. Principle of the stereoscope



FIG. 437. The Zeiss binocular

A further advantage which is gained by the Zeiss binocular is due to the fact that the two objectives are separated by a distance which is greater than the distance between the eyes, so that the stereoscopic effect is more prominent than with the unaided eye or with the ordinary opera glass.*

462. The periscope. A periscope is a sort of double-jointed telescope which makes use of total reflection twice, at the top and at the bottom. The system of lenses gives a magnification of about 1 diameters, as




FIG. 438. A parabolic reflector

this has been found best to make ships appear at their true distances from the submarine. There is no stereoscopic effect, since the periscope is not double like a binocular.

463. Parabolic reflectors. For the projection of a more nearly cylindrical beam than is possible with spherical mirrors, it is customary to use parabolic reflectors, as in automobile headlights (Fig. 438, (1) and (2)). The light is placed a little closer to the reflector than the principal focus, so that the reflected light may spread somewhat. The same principle is employed in searchlights, except that the source of light (usually a powerful arc) is kept more nearly at the principal focus of the reflector. The Sperry 60-inch searchlight, the most powerful in the world, has a beam candle power of approximately two thirds that of the sun, and its light is plainly visible at a distance of one hundred miles.

* Laboratory experiments on the magnifying powers of lenses and on the construction of microscopes and telescopes should follow this chapter. See for example, Experiments 47, 48, and 49 of the authors' Manual.


1. Why is it necessary for the pupils of your eyes to be larger in a dim cellar than in the sunshine? Why does the photographer use a large stop on dull days in photographing moving objects?

2. If a photographer wishes to obtain the full figure on a plate of cabinet size, does he place the subject nearer to or farther from the camera than if he wishes to take the head only? Why?

3. A child 3 ft. in height stood 15 ft. from a camera whose lens had a focal length of 18 in. What was the distance from the lens to the photographic plate and the length of the child's photograph?

4. If 20 sec. is the proper length of exposure when you are printing photographs by a gas light 8 in. from the printing frame, what length of exposure would be required in printing from the same negative at a distance of 16 in. from the same light?

5. If a 20-second exposure is correct at a distance of 6 in. from an S-candle-power electric light, what is the required time of exposure at a distance of 12 in. from a 32-candle-power electric light?

6. The image, on the retina, of a book held a foot from the eye is larger than that of a house on the opposite side of the street. Why do we not judge that the book is actually larger than the house?

7. What sort of lenses are necessary to correct shortsightedness? longsightedness? Explain with the aid of a diagram.

8. What is the magnifying power of a 4-in. lens used as a simple magnifier?

9. If the length of a microscope tube is increased after an object has been brought into focus, must the object be moved nearer to or farther from the lens in order that the image may again be in focus?

10. Explain as well as you can how a telescope forms the image that you see when you look into it.

11. Is the image on the retina erect or inverted?




464. Wave lengths of different colors. Let a soap film be formed across the top of an ordinary drinking glass, care being taken that both the solution and the glass are as clean as possible. Let a beam of sunlight or the light from a projecting lantern pass through a piece of red glass at A, fall upon the soap film F, and be reflected from it to a white screen S (see Fig. 439). Let a convex lens L of from 6 to 12 inches focal length be placed in the path of the reflected beam in such a position as to produce an image of the film upon the screen S, that is, in such a position that film and screen are at conjugate foci of the lens. The system of red and black bands upon the screen is formed precisely as in § 427, by the interference of the two beams of light coming from the front and back surfaces of the wedge-shaped film. Now let the red glass be held in one half of the beam and a piece of green glass in the other half, the two pieces being placed edge to edge, as shown at A. Two sets of fringes will be seen side by side on the screen. The fringes will be red and black on one side of the image, and green and black on the other; but it will be noticed at once that the dark bands on the green side are closer together than the dark bands on the other side; in

FIG. 439. Proje on of soap-film fringes



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