When an electromagnetic wave, consisting of moving electric and magnetic lines, strikes a conductor, induced electromotive forces are produced. For example, imagine, in the case of Figs. 351 and 352, that there is another vertical wire at some distance from A. When the magnetic and electric lines radiated by A strike this second aërial, they will induce an electromotive force in it. Further, since the magnetic and electric lines oscillate, having first one direction and then the opposite, the induced electromotive force in the second aërial will act up and then down, oscillating with the same frequency as the current in the first aërial. Thus the first principle involved in the detection of electromagnetic waves is that these waves induce oscillatory electromotive forces in conductors which they strike.

The second principle used is that of resonance. The receiving circuit is adjusted until its natural frequency is the same as the frequency of the incoming wave. When in "tune" the induced currents will be relatively large, and can be measured, or detected, by suitable instruments.

PROBLEMS

1. Compute the natural frequency of oscillation of a circuit consisting of a 0.015-microfarad condenser in series with an inductance of 0.0002 henry.

2. A circuit consisting of a 1-microfarad condenser in series with an inductance has an oscillation frequency of 1000 per second. What is the value of the inductance ?

3. A condenser is in series with an inductance of 1.0 henry. What must be the value of the capacitance in order that this combination may be in resonance with the commercial 60-cycle alternating current?

4. What must be the frequency of oscillation of a circuit that produces electromagnetic waves 1000 m. long?

4

5. What must be the natural frequency of oscillation of a receiving circuit

in order that it may be in tune with a 400-meter wave?

PART V. LIGHT

CHAPTER XL

PROPAGATION AND PHOTOMETRY

Radiation of light, 557. The pinhole camera, 558. The inverse-square law, 559. Derivation of the inverse-square law, 560. Photometry, 561. The photometer, 562. Theories of light, 563. Velocity of light, 564. Römer's method, 565. Bradley and the aberration of light, 566. Foucault's method, 567.

557. Radiation of light. Early childhood experience teaches us certain things about light. Among these may be noted the following:

1. Only when a source of light is present can other objects be seen. There is a difference between self-luminous bodies and those which give light by reflection. Most objects are seen by the light which they reflect to the eye.

2. Some objects, like window glass, are transparent and freely transmit light; while others milk glass, for example-are translucent (that is, they transmit light, but not so that one can see objects distinctly through them). But the great majority of substances are opaque; that is, they do not transmit light except when very thin layers are used.*

3. Light is propagated in sensibly straight lines; that is, light, except in special cases, travels in a straight line from an object to the eye. Measurements in surveying, navigation, and astronomy prove that this is accurately true. This property of light is usually referred to as "the rectilinear propagation of light."

558. The pinhole camera. When light passes through a small opening in a darkened room, inverted images of objects out of doors will be formed on the wall opposite the opening. Light from a candle flame passing through a small hole in a screen will form an inverted image on a second screen (Fig. 353). A box with a small hole in one side is often called a pinhole camera. The formation of an image by the light which passes through a small hole is due to the fact that light from different parts of an object travels in practically straight lines through the hole. The student should supply the details and become certain that he understands why an image is formed.

The shadows of trees cast by sunlight usually have bright patches in them caused by the sunlight coming through small openings between the leaves. The small patches are round images of the sun. Why? At the time of a partial eclipse, when the sun is nearly covered, these images are crescent-shaped; that is, of the same shape as the visible part of the sun. 559. The inverse-square law. The intensity of illumination of a given surface is equal to the amount of light that falls on a unit area of the surface

in a unit of time. This statement by

FIG. 353

itself is not clear, for it does not explain what is meant by the expression "amount of light." Sometimes this expression means the amount of energy, measured in ergs, in the radiation; but usually the amount of light is measured in special units which take account of the corresponding sensation produced in the eye. It is not necessary, however, to understand this point fully now. The important part of this definition to be noted now is that intensity of illumination refers to unit area.

A very simple law connecting the intensity of illumination of any surface (a book, for example) with the distance of the surface from the source is as follows: The intensity of illumination of any surface varies inversely as the square of the distance of the surface from the source.

For example, if a book is held 6 feet from a source of light, and the distance is then reduced to 3 feet, the following proportion is true:

Intensity at 6 feet 32

9

1

Hence the intensity of illumination at a distance of 3 feet from the source is four times that at 6 feet.

This law is accurately true only when the dimensions of the source are small compared with the other distances involved. For practical purposes the law is sufficiently accurate when the distance of the surface from the source is ten times the largest dimension of the source; for example, if the bright filaments of an incandescent lamp are

a'

Fig. 354 the source of light is at S. Consider only the light which passes through the imaginary rectangular surface abcd. Since light travels in straight lines, the same light will pass through the larger area a'b'c'd', where the points a', b', c', and d' lie on straight lines passing through a, b, c, and d respectively and through the source S (for simplicity the surface a'b'c'd' is taken parallel to the surface abcd).

Let r1 be the shortest distance of abcd from S and let r2 be the distance of a'b'c'd'. From the geometry of similar triangles,

But the numerator of the left-hand side is the area of the rectangular surface abcd, and the denominator the area a'b'c'd'; hence,

Let Q be the quantity of light passing through the area abcd and the area a'b'c'd' in 1 second. From the definition of intensity of illumination,

Intensity of illumination of abcd =

(2)

But the right-hand side is, from equation (1), equal to the ratio of the squares of the distances from the source;

561. Photometry. That branch of the subject of light which deals with the measurement of the luminous intensity of different sources of light and with the illumination produced by various sources is called photometry. A few of the quantities which are used and some of the simpler methods of measuring them will be explained.

The luminous intensities of different sources of light are measured in terms of candle power. The international candle is an arbitrary unit for measuring luminous intensity. A special group of incandescent lamps the candle power of which is known is maintained by the Bureau of Standards in conjunction with similar institutions abroad. Anyone may buy an incandescent lamp the candle power of which has been determined by a direct or an indirect comparison with these standards. This lamp can then be used as a standard to measure the candle power of other sources. The unit for measuring intensity of illumination of any surface is so defined that

Intensity of illumination =

candle power of source square of distance from source

When the distance is measured in feet, the intensity of illumination is expressed in foot-candles. For example, at a distance of 4 feet from a lamp having a luminous intensity of 24 candle power, the intensity of illumination is