photographs are mounted at A and B (Fig. 444), 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 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 whereas telescopes are usually constructed with one tube, opera glasses always have two, one for each eye.

m

n

FIG. 444. Principle of the stereoscope

460. The prism 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 prism binocular (Fig. 445) 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 totalreflecting 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.

A further advantage which is gained by the prism binocular is due to the fact that the two objectives are separated by a distance

which is greater than the distance between the eyes; hence the stereoscopic effect is more prominent than with the unaided eye or with the ordinary opera glass.*

SUMMARY. The camera, the projection lantern, and the eye form real images on screens.

The magnifying power of the microscope, the telescope, the opera glass, and the field glass is due to the increase they produce in the visual angle.

The magnifying power of a single lens is considered equal to the ratio of 25 centimeters (or 10 inches) to the focal length of the lens.

The magnifying power of the telescope and of the opera glass is equal to the ratio of the focal length of the objective to that of the eyepiece.

The magnifying power of a compound microscope is the product of the magnifying power of the objective and that of the eyepiece.

QUESTIONS AND PROBLEMS†

1. If a pinhole camera is 8 in. long and the image of a building 50 ft. high appears as an image 3 in. high on the plate, how far away is the building?

2. How tall is a tree 200 ft. away if the image of it formed by a camera lens of focal length 4 in. is 1 in. long? (Consider the image to be formed in the focal plane.)

3. How long an image of the same tree will be formed in the focal plane of a lens having a focal length of 9 in.?

4. When a camera is adjusted to photograph a distant object, what change in the length of the bellows must be made to photograph a near object? Explain clearly why this adjustment is

necessary.

5. From Fig. 446 explain the camera view finder, F being the principal focus of the objective and F' that of the eyepiece.

* Laboratory experiments on the magnifying powers of lenses and on the construction of microscopes and telescopes should follow this chapter. See, for example, Experiments 60, 61, and 62 of "Exercises in Laboratory Physics," by Millikan, Gale, and Davis.

† Supplementary questions and problems for Chapter XIX are given in the Appendix.

6. Explain why both near and distant objects can be satisfactorily photographed with a small fixed-focus camera.

7. The projection lens of a lantern has a focal length of 1 ft. How far back of the lens must a slide be placed in order to focus clearly upon the screen 24 ft. from the lantern?

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

9. 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?

Objective

F

Eyepiece

Mirror

FIG. 446. View-finder

of camera

10. What sort of lenses are necessary to correct nearsightedness? farsightedness? Explain with the aid of a diagram.

11. Given a spectacle lens, how could you determine whether it is a converging or a diverging lens?

12. What is the magnifying power of a 1-inch lens used as a simple magnifier?

Arc

F

FIG. 447. Principle of the spotlight

13. Fig. 447 represents a theater spotlight projector adjusted to illuminate a small part of the stage. How must the arc be moved to illuminate a larger area on the stage? (F is the principal focus of the plano-convex lens.)

14. A telescope has an objective whose focal length is 30 ft. and an eyepiece whose focal length is 1 in. What is the magnifying power of the telescope?

CHAPTER XX

COLOR PHENOMENA

COLOR AND WAVE LENGTHS

Red

Green

S

461. 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. 448). Let a convex lens L of from six to twelve 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

(Green

Red

upon the screen is formed FIG. 448. Projection of soap-film fringes precisely as in § 428, 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 fact, seven fringes on

the side of the film which is covered by the green glass will be seen to cover about the same distance as six fringes on the red side.*

Since it was shown in Fig. 388 that the distance between two dark bands corresponds to an increase of one-half wave length in the thickness of the film, we conclude, from the fact that the dark bands on the red side are farther apart than those on the green side, that red light must have a longer wave length than green light. The wave length, number of waves per centimeter, and rate of vibration of the central portion of each colored region of the spectrum are roughly as follows:

Let the red and green glasses be removed from the path of the beam. The red and green fringes will be seen to be replaced by a

series of bands brilliantly colored

in different hues. These are due to the fact that the lights of different wave length form interference bands at different places on the screen. Notice that the upper edges of the bands (lower edges in the inverted image) are reddish, whereas the lower edges are bluish. We shall find the explanation of this fact in § 470.

FIG. 449. White light dispersed by a prism

462. Composite nature of white light shown by dispersion. Let a beam of sunlight pass through a narrow slit and fall on a prism, as in Fig. 449. The beam which enters the prism as white light is

* The experiment may be performed at home by simply looking through red and green glasses at a soap film so placed as to reflect white light to the eye.