5. Formation of images by small apertures.

Exercises

1. Consider the circ.u.mference of the earth as 25,000 miles. How many times would the speed of light cover this distance in a second?

2. How soon after any great disturbance takes place on the sun, 93,000,000 miles distant, can it be seen upon the earth?

3. Construct a diagram of the moon's shadow. How much of the sun can one see when in the moon's umbra? When in its penumbra? Have you ever been in either? When? Have you ever been in the earth's umbra? In its penumbra?

4. Explain, using a diagram, the formation of an inverted image by a small aperture.

5. If the sun is 45 degrees above the horizon, what is the height of a pole casting a shadow 60 ft. long?

6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically upon a walk, how tall is the tree whose shadow is 42 ft. long, both measurements being made at the same time?

7. Why are the shadows caused by an electric arc lamp so sharply defined?

8. Why should schoolroom windows be all on one side and reach to the ceiling?

9. What is the relation between the size of an image and its distance from the aperture forming it? Can you prove this by geometry?

10. What are silhouettes and how are they produced?

(2) PHOTOMETRY AND THE LAW OF REFLECTION

=358. Photometry.=--It is desirable at times to compare the intensities of illumination produced by light from different sources. This is done to determine the _relative cost or effectiveness_ of various illuminants such as candles, kerosene and gas lamps, and electric lights The process of determining the relative intensity of lights or lamps is called photometry. (_Photos_ = light.)

The unit for measuring the power of light is called a _candle power_. It is the light produced by a sperm candle burning 120 grains per hour. An ordinary gas light burns 5 or more cubic feet of gas per hour and yields from 15 to 25 candle power. A Welsbach gas lamp, consuming 3 cu. ft. per hour, produces 50 to 100 candle power.

Instead of using candles, for practical photometry, incandescent lamps standardized by the Bureau of Standards are used for testing or calibration purposes.

It is necessary to distinguish between the intensity of a _luminous_ body, _i.e._, as a source of light, and the _intensity_ of _illumination_ upon some surface produced by a light. It is considered that two sources of light are of _equal intensity_ if they produce equal illumination at equal distances.

=359. Law of Intensity of Light.=--A device for measuring the candle power of a light is called a _photometer_. Its use is based upon the _law of intensity of light_. _The intensity of illumination of a surface is inversely proportional to the square of its distance from the source of light._ This relation is similar to that existing between the intensity of a sound and the distance from its source. The following device ill.u.s.trates the truth of this law in a simple manner.

[Ill.u.s.tration: FIG. 350.--The light spreads over four times the area at twice the distance.]

Cut a hole 1 in. square in a large sheet of cardboard (_K_) and place the card in an upright position 1 meter from an arc light or other _point source_ of light (_L_). Now rule inch squares upon another card (_M_) and place it parallel to the first card and 2 meters from it. (See Fig. 350.) The light that pa.s.sed through the hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq.

in. at a distance of 2 meters. Therefore, the intensity of illumination on each square inch of _M_ is one-fourth that upon the surface of _K_. If _M_ is placed 3 meters from the light, 9 sq. in.

are illuminated, or the intensity is one-ninth that at 1 meter distance.

[Ill.u.s.tration: FIG. 351.--The Bunsen photometer.]

These relations show that the intensity of illumination is inversely proportional to the square of the distance from the source of light. An application of the law of intensity is made in using a simple (Bunsen) photometer. This consists of a card containing a spot soaked with oil or melted wax. (See Fig. 351.) The lights whose intensities are to be compared are placed upon opposite sides of the card. The card is then adjusted so that the spot appears the same on both sides. The illumination is now equal on both sides of the card and the _candle powers of the two lights are proportional to the squares of their distances from the card_. The simple device just described will give approximate results only. For accurate results more elaborate apparatus is required.

=360. Measurement of the Intensity of Illumination.=--A standard candle (Art. 358) produces when lighted 1 candle power. The illumination caused by this upon a surface 1 ft. away and at right angles to the light rays is called a =foot-candle=. It is the unit of intensity of illumination.

A 4-candle-power lamp, at a distance of 1 ft., produces 4 foot-candles.

A 16-candle-power lamp at a distance of 2 ft. also produces 4 foot-candles--(16 2).

The intensity of illumination required for a good light for seeing varies with the conditions. Thus, for stage and store lighting about 4 foot-candles are needed, while homes and churches may require but 1 foot-candle.

Too great an intensity of illumination is as harmful as not enough.

Exposed lights having an intensity of more than 5 candle power per square inch are often a cause of eye trouble. Such lights should be protected by frosted globes.

A pleasing form of lighting for large halls and public buildings is the _indirect system_. In this, the lamps are hidden by reflectors which throw the light upon the ceiling from which it is diffused over the room. This form of lighting is more expensive than other systems since but a part of the light is reflected. Its cost therefore is an important factor when considering its use.

=361. The Reflection of Light.=--The light reflected from the surfaces of bodies about us gives us information concerning our surroundings. A knowledge of the behavior of light undergoing reflection is not usually gained from ordinary observation. The law of reflection of light may be shown, however, by an experiment.

[Ill.u.s.tration: FIG. 352.--_B'_ is as far back of the mirror as _B_ is in front of it.]

[Ill.u.s.tration: CHRISTIAN HUYGENS

(Popular Science Monthly)

Christian Huygens (1629-1695). Dutch physicist; invented the pendulum clock (1656); developed the wave theory of light; discovered polarization of light (1690).]

[Ill.u.s.tration: H. V. HELMHOLTZ

"By Permission of the Berlin Photographic Co., New York."

Hermann von Helmholtz (1821-1894) Germany. Established the doctrine of conservation of energy; made many discoveries in sound; invented the ophthalmoscope; established the physical basis of tone quality.]

A plane mirror, _M_, is held in a vertical position resting upon a sheet of paper. (See Fig. 352.) Pins are set upright in the paper at _A_ and _B_. On placing the eye along the line _AC_ and looking toward the mirror an image of _B_ may be seen in the mirror due to the light reflected from its surface. Pins _C_ and _D_ are now set in the paper so that when one looks along the line _BD_ toward the mirror one may see all four pins apparently in one line. This indicates that the light from _A_ and _C_ pa.s.sing along _CA_ toward _O_ is reflected back along the light _CBD_. By means of a ruler, draw lines through _BD_ and _AC_ till they intersect at _O_. Also draw _PO_ perpendicular to the mirror at _O_.

Then the angles _AOP_ and _BOP_ will be found equal. These are called the angles of _incidence_ and _reflection_ respectively. _The law of reflection_ is therefore stated: _The angle of reflection is equal to the angle of incidence._ These angles are in the same plane, that of the paper. This law applies in all cases of reflection of light. It is similar to the law of reflection of sound (Art. 326.)

Important Topics

1. Photometry, law of intensity, candle power, foot-candle.

2. Intensity of illumination.

3. Reflected light and law of reflection.

Exercises

1. Both sides of a card are equally illuminated when two lights are on opposite sides of it and 10 and 30 cm. respectively from it. what are their relative intensities?

2. What are the relative intensities of illumination from a gas light upon a book 6 ft. and 2 ft. respectively from the light?

3. Which is more expensive per candle power? How many times as expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of gas per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per hour, and then the cost of 1 candle power hour for each.)

4. Why are not ordinary shadows perfectly dark?