CHAPTER XVIII

NATURE AND PROPAGATION OF LIGHT

TRANSMISSION OF LIGHT

418. Speed of light. Before the year 1675 light was thought to pass instantaneously from the source to the observer. In that year, however, Olaus Römer, a young Danish astronomer, made the following observations. He had observed accurately the in

stant at which a satellite of Jupiter, M (Fig. 378), passed into Jupiter's shadow when the earth was at E, and he forecast, from the known mean time between such eclipses, the exact instant at which a given eclipse ought to occur six months

JO

FIG. 378. Illustrating Römer's determination of the velocity of light

later, when the earth should be at E'. It actually took place 16 minutes 36 seconds (or 996 seconds) later. Römer concluded that the 996 seconds' delay represented the time required for light to travel across the earth's orbit, a distance known to be about 180,000,000 miles. The most precise of modern determinations of the speed of light are made by laboratory methods. The generally accepted value, that of Michelson, of The University of Chicago, is 299,800 kilometers per second. It is sufficiently correct to remember it as 300,000 kilometers, or 186,000 miles. Though this speed

would carry light around the earth 7 times in a second, yet it is so small in comparison with interstellar distances that the light which is now reaching the earth from the nearest fixed star, Alpha Centauri, started 4.3 years ago. If an observer on the pole star had a telescope powerful enough to enable him to see events on the earth, he would not have seen the battle of Gettysburg (which occurred in July, 1863) until January, 1918. The distances of some of the spiral nebulæ have recently been measured by E. P. Hubble of the Mt. Wilson Observatory, who finds them to be so astoundingly remote from us that the light by which we now see these nebulæ started about one million years ago.

Both Foucault in France and Michelson in America have measured directly the velocity of light in water and have found it to be only three fourths

as great as in air. It will be shown later that in all transparent liquids and solids it is less than it is in air.

I

419. Reflection of light.* Let a beam of sunlight be admitted to a darkened room through a narrow slit. The straight path of the beam will be rendered visible by the brightly illumined dust particles suspended in the air. Let the beam fall on the surface of a mirror. Its direction will be seen to be sharply changed, as shown in Fig. 379. Let the mirror be held so that it is perpendicular to the beam. The beam will be seen to be reflected directly back on itself. Let the mirror be turned through an angle of 45°. The reflected beam will move through 90°.

The experiment shows roughly, therefore, that the angle IOP, between the incident beam and the normal to the mirror, is equal to the angle POR, between the reflected beam and the normal to the mirror. The first angle, IOP, is called

* An exact laboratory experiment on the law of reflection should either precede or follow this discussion. See, for example, Experiment 54 of "Exercises in Laboratory Physics," by Millikan, Gale, and Davis.

the angle of incidence, and the second, POR, the angle of reflection. The angle of reflection is equal to the angle of incidence.

420. Diffusion of light. In the last experiment the light was reflected by a very smooth plane surface. Now let the beam be allowed to fall upon a rough surface like that of a sheet of unglazed white paper. No reflected beam will be seen; but instead the whole room will be brightened appreciably, so that the outline of objects before invisible may be plainly distinguished.

The beam has evidently been scattered in all directions by the innumerable little reflecting surfaces of which the surface of the paper is composed. The effect will be much more noticeable if the

beam is allowed to fall alternately on a piece of dead-black cloth and on the white paper. The light

FIG. 380. Regular and irregular reflection

is largely absorbed by the cloth, whereas it is scattered or diffusely reflected by the paper. Illumination sufficiently strong for sewing on white material may be altogether too weak for working on black goods. The difference between a smooth reflector and a rough one is illustrated in greatly magnified form in Fig. 380. The air shafts of apartment houses are made white to get the maximum diffusion of daylight into rooms that might otherwise be very dark.

421. Visibility of nonluminous bodies. Everyone is familiar with the fact that certain classes of bodies, such as the sun, a gas flame, etc., are self-luminous (visible on their own account), whereas other bodies, like books, chairs, tables, etc., can be seen only when they are in the presence of luminous bodies. The above experiment shows how such nonluminous, diffusing bodies become visible in the presence of luminous bodies. For, since a diffusing surface scatters in all directions the light which falls upon it, each small element of such a surface is sending out light in a great many directions, in much the

same way in which each point on a luminous surface is sending out light in all directions. Hence we always see the outline of a diffusing surface as we do that of an emitting surface, no matter where the eye is placed. On the other hand, when light comes to the eye from a polished reflecting surface, since the form of the beam is wholly undisturbed by the reflection, we see the outline not of the mirror but rather of the source from which the light came to the mirror, whether this source is itself self-luminous or not. All bodies other than selfluminous ones are visible only by the light which they diffuse. Black bodies send no light to the eye, but their outlines can be distinguished by the light which comes from the background. Any object which can be seen, therefore, may be regarded as itself sending rays to the eye; that is, it may be treated as a luminous body.

FIG. 382. Shadow from a small source

422. Shadows. Let any opaque object be held very close to a white screen placed opposite a window or a broad gas flame. So long as the object is very close to the screen the shadow is uniformly dark, but as it is moved toward the source of light (F, Fig. 381) two parts to the shadow will be observed: a very black part, cd, in the middle, from which all the light from the source is excluded; and a part, ec and df, which grows gradually lighter with distance from the dark center cd.

Sun

Earth Moon

FIG. 383. Illustrating a total eclipse of the moon by passage into the umbra of the earth

These effects are easily explained on the basis of the rectilinear propagation of light. The region abdc, from which the

light from all points of the source mn is excluded, is called the umbra. The region ace and bdf, which receives light from some portions of the source but not from all, is called the penumbra. It will be seen from the figure that the penumbra must decrease as the object approaches the screen, and also as the size of the source diminishes. When the source becomes a mere point there is no penumbra at all (Fig. 382). When the source is larger than the opaque object, as in the case of the sun and earth, the umbra is a cone, as shown in Fig. 383.

SUMMARY. The velocity of light is 300,000 kilometers per second, or 186,000 miles per second.

The angle of reflection equals the angle of incidence.
Diffusion of light is its irregular reflection.

Nonluminous bodies are seen by the light which they diffuse. A perfect reflector would be invisible.

QUESTIONS AND PROBLEMS

1. Sirius, the brightest star, is about 52,000,000,000,000 miles away. If it were suddenly annihilated, how long would it shine on for us?

2. Devise an arrangement of mirrors by means of which you could see over and beyond a high stone wall or trench embankment. This is a very simple form of periscope.

3. Why is a room with white walls much lighter than a similar room with black walls?

4. Compare the reflection of light from white blotting paper with that from a plane mirror. Which of these objects is more easily detected from a distance? Why?

5. Show by a diagram the relative positions of the earth, the sun, and the moon during a total eclipse of the moon, indicating by lines the umbra of the earth and by a dot the position of the observer.

6. Explain a total eclipse of the sun by the method used in question 5. Explain similarly a partial eclipse of the sun.

7. Will it ever be possible for the moon totally to eclipse the sun from the whole of the earth's surface at once?