S1. A small opening in this screen allowed the light of one color to pass through and fall on a second prism, P2. After passing through this prism, it fell on the screen S2. Newton found that the light which passed through the second prism P2 was not separated into different colors. For example, if green light passed through the hole in the first screen, only green light was seen on the second screen; if the first screen was moved so that some other color, say red, passed through the hole, only red would be seen on the second screen. In this way Newton showed that the first prism resolved white light into parts which could not be further separated by a second prism. In other words, a prism can separate light into components each of which is homogeneous (not a mixture).

B

B'

A'

A

599. Atmospheric refraction of light. The velocity of light in air is slightly less than that in free space. The denser the air the less is the velocity. Light which reaches us from celestial objects travels down through an atmosphere of increasing density, and its velocity gradually changes as it approaches. When the light comes from directly overhead, there will be no refraction, or bending; but when the light

FIG. 397

comes from objects in other portions of the sky, there will be a change in its direction. As shown in Fig. 397, the bending is in such a direction that the object is apparently displaced toward the zenith; light coming from the direction A is bent so that it appears to come from A', and that from B appears to come from B'. The bending is very small except for objects located near the horizon. At an angular elevation of 45 degrees the displacement is about one thirtieth of the diameter of the moon; at an angular elevation of 15 degrees it is about one sixth the diameter of the moon. This increase of bending as objects get nearer the horizon is the cause of the apparent flattening of the sun and the moon at the horizon. The lower edge is raised more than the top, which makes the vertical diameter appear less than the horizontal one. The refraction at the horizon is enough to make an appreciable difference in the apparent time of the rising and the setting of the sun or moon. Inasmuch as the moon or the sun at the horizon is apparently raised by refraction by an amount a little more than its diameter, we can see the moon or the sun when it is really below the horizon.

When one looks over a hot radiator or a hot pavement, there is seen a wavy, shimmering effect. The density of hot air is less than that of cold air, and light travels faster in it when it is hot than when it is cold. For this reason, when a beam of light passes from cold air to hot air or from hot air to cold air, it is bent. Thus a ray of light passing over a hot radiator is bent in passing through the heated air. If this heated air would remain quiet, the amount that the light is bent would remain constant. But the hot air does not do this, it is in constant motion. Moreover, it is being mixed with colder air, with the result that its density is continually changing. For this reason the amount that the ray is bent is varying continuously. Hence the apparent position of an object seen through this heated air is changing back and forth or up and down in a very irregular way. It is commonly said that one sees the "heat waves" rising. That is not so. The effect is caused by the change in the amount that light is bent as it travels through air of different densities. The same thing can be seen in looking through a glass vessel of water into which glycerin or alcohol is being poured.

The twinkling, or scintillation, of stars is due to the unstable condition of the air through which the light comes, and hence to the change in the amount that the light is bent. Since there is a slight difference in the velocity of different colors, these may be bent differently, and there may be changes in the color of the star as it twinkles. Light from distant terrestrial sources of light will often twinkle when there is a mixing of warm and cool air currents between the source and the observer.

When currents of warm and cold air are mixing on a large scale, there is considerable interference with good seeing. This is of very great importance in telescopic work. It is sometimes called optical haze and distinguished from dust haze. It may be very noticeable on hot days, even when the air is comparatively free from dust.

A number of rather curious distortions of distant objects near the horizon occur under special conditions. Among these distortions are the phenomena known as looming, towering, sink

ing, and stooping.* They can all

be explained by refraction.

FIG. 398

600. The mirage. A number of different optical effects, known under the general name of mirage, are due to atmospheric refraction. Only one kind, known as the inferior mirage, will be explained here- the kind most commonly observed.

Under special circumstances, as in the case of a heated pavement or a dry plain, the density of the air is less near the surface. In that case lightwaves are refracted as shown in an exaggerated way in Fig. 398. In Fig. 399

* See Humphrey's "Physics of the Air."

Some light
The result

the eye is at E. Light from the sky coming down over the tree tops enters the hot air near the heated pavement and is bent up to the eye. from the trees will travel straight across through the cooler air. is that some of the sky will be seen apparently below the trees. Sky seen in that direction will appear as sky reflected in water. In some cases the light from the trees which travels

down toward the pavement may be bent up, and thus one will apparently see images of trees in the water. On a bright, clear day it is usually possible to find some street or pavement which, when

E

FIG. 399

one stoops down and looks along it, will show some sky light below the distant trees or other objects. It is a common experience of motorists, on clear days, for a paved roadway some distance in front of them to appear covered with water.

PROBLEMS

1. The angle of incidence on glass is 50°, and the observed angle of refraction is 35°. Find the index of refraction. (sin 50° = 0.766; sin 35° = 0.574.) 2. The angle of incidence of light on water, index 1.33, is 30°. Find the sine of the angle of refraction.

3. Light which emerges from water, index 1.33, has an angle of incidence in the water of 40°. Find the sine of the angle of refraction.

4. The index of refraction of a certain kind of glass is 1.5. Compute the speed of light in this glass.

5. For light which has a wave-length in air of 0.00006 cm., what would be the wave-length in glass the index of which is 1.5?

6. A block of glass the index of which is 1.5 is completely submerged in water (index 1.33). Light strikes the glass at an angle of incidence of 30°. Compute the sine of the angle of refraction in the glass.

7. A 60°-prism of crown glass, index 1.5, is submerged in carbon bisulfide, the index of which is 1.6. Make a diagram showing the approximate path of a ray of monochromatic light through the prism.

8. Draw a diagram similar to that requested in Problem 7, but for the case of the prism submerged in water, the index of which is 1.33.

CHAPTER XLIII

LENSES

Converging and diverging lenses, 601. The principal axis of a lens, 602. The principal focus, 603. The optical center, 604. Graphical construction of images, 605. The quantitative law of position of image, 606. Derivation of the quantitative law, 607. The quantitative law applied to diverging lenses, 608. Summary of rules for use of signs in the quantitative law, 609. Law of size of image, 610. Two thin lenses in contact, 611. The power of a lens; the dioptric, 612. Spherical aberration, 613. Chromatic aberration, 614. Astigmatism, 615. Distortion of images, 616.

601. Converging and diverging lenses. When a beam of parallel light passes through a lens having convex surfaces (Fig. 400), the beam is converged to a

focus. A lens of this type is said to be a converging lens. But when a beam of parallel

light passes through a lens hav

ing concave faces (Fig. 401),

the emerging beam diverges,

FIG. 400

F

and the focus is a virtual one. Such a lens is called a diverging lens.

It is very important to understand the cause of these effects.

The converging or diverging power of lenses depends on the fact that light travels more slowly in glass than in air. In the beam incident on the lens of Fig. 402 the waves are shown by the straight parallel lines. Because light

F

FIG. 401

travels more slowly in glass than in air, that part of the waves which travels through the thicker portions of the lens is retarded more than the part which travels through the thinner portions; hence the emerging waves are curved as shown in the figure. For thin lenses with spherical surfaces the emerging waves will be spherical, except in cases explained later (sect. 615). Since light always travels perpendicularly to the waves, it converges to their center of curvature (F in the figure).

In a diverging lens the glass is thinner at the center and thicker near the edges; hence the central portion of each wave gets ahead

(Fig. 403). Since light travels perpendicularly to the waves, the beam diverges from their center of curvature (F in the figure). From the foregoing explanations it should be clear that in a converging lens the glass is thicker at the center, and that in a diverging lens it is thinner at the center. This statement is a rule for telling which lenses are converging and which diverging. In Fig. 404 are examples of both

types.

602. The principal axis of a lens. The principal axis of a lens is a line drawn through the center of the lens and the cen

ters of curvature of the faces.

FIG. 404

603. The principal focus. The principal focus of a lens is defined in a manner similar to that used for mirrors. The principal focus of a lens is the point which is the focus when the incident light is a beam parallel to the axis (Figs. 400 and 401).

In a converging lens the principal focus is real (Fig. 400); in a diverging lens it is virtual (Fig. 401). If a point source of light could be placed at the principal focus of a converging lens, the light, after going through the lens, would form a parallel beam.