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11. How far from a screen must a 4-candle-power light be placed to give the same illumination as a 16-candle-power electric light 3 m. away? 12. If two plane surfaces placed 1 m. and 2 m. respectively from a given light receive perpendicularly the same quantity of light, how must their areas compare? State the law involved.
13. If two foot-candles are desired for reading, at what distance from the book must a 32-candle-power lamp be placed?
CHAPTER XIX. 1. An object 5 cm. long is 50 cm. from a concave mirror of focal length 30 cm. Where is the image, and what is its size? 2. Describe the image formed by a concave lens. Why can it never be larger than the object?
3. What is the focal length of a lens if the image of an object 10 ft. away is 3 ft. from the lens?
4. If the object in Problem 3 is 6 in. long, how long will the image be?
5. A beam of sunlight falls on a convex mirror through a circular hole in a sheet of cardboard, as in Fig. 487. Prove that when the diameter of the reflected beam rq is twice the diameter of the hole np, the distance mo from the mirror to the screen is equal to the focal length oF of the mirror.
6. If a rose R is pinned upside down in a brightly illuminated box, a real image may be formed in a glass of water W by a concave mirror C (Fig. 488). Where must the eye be placed to see the image?
7. How far is the rose from the mirror in the arrangement of Fig. 488?
8. A candle placed 20 cm. in front of a concave mirror has its image formed 50 cm. in front of the mirror. Find the radius of the mirror.
FIG. 487. Determination of focal length of a convex mirror
FIG. 488. Image of object at center of curvature
9. The parabolic mirror used as an objective in one of the telescopes at the Mount Wilson observatory is 100 in. in diameter and has a focal el length of about 50 ft. What magnification is obtained when it is used with a 2-inch eyepiece; with a 1-inch eyepiece? What is gained by the use of a mirror of such enormous diameter?
10. A compound microscope has a tube length of 8 in., an objective of focal length in., and an eyepiece of focal length 1 in. What is its magnifying power?
11. If the focal length of the eye is 1 in., what is the magnifying power of an opera glass whose objective has a focal length of 4 in.?
12. Explain as well as you can how a telescope forms the image which you see when you look into it.
13. The magnifying power of a microscope is 1000, the tube length is 8 in., and the focal length of the eyepiece is in. What is the focal length of the objective?
CHAPTER XX. 1. If a soap film is illuminated with red, green, and yellow strips of light, side by side, how will the distance between the yellow fringes compare with that between the red fringes? with that between the green fringes? (See table on page 403.)
2. What will be the apparent color of a red body when it is in a room to which only green light is admitted?
3. Will a reddish spot on an oil film be thinner or thicker than an adjacent bluish portion?
4. Explain the ghastly appearance of the face of one who stands under the light of a Cooper-Hewitt mercury-vapor arc lamp.
5. Draw a figure to show how a spectrum is formed by a prism, and indicate the relative positions of the red, the yellow, the green, and the blue in this spectrum.
6. Why is a rainbow never seen during the middle part of the day? 7. If you look at a broad sheet of white paper through a prism, it will appear red at one edge and blue at the other, but white in the middle. Explain why the middle appears uncolored.
8. Can you see any reason why the vibrating molecules of an incandescent gas might be expected to give out a few definite wave lengths, while the particles of an incandescent solid give out all possible wave lengths?
9. Can you see any reason why it is necessary to have the slit narrow and the slit and screen at conjugate foci of the lens in order to show the Fraunhofer lines in the experiment of § 480?
CHAPTER XXI. 1. How are ultra-violet waves detected? What apparatus is used to reveal infra-red waves?
2. Explain how the heat of the sun warms the earth.
3. What is electric resonance? How may it be demonstrated?
4. Describe the construction of an X-ray tube. Describe as well as you can the action within it when in use.
Aberration, chromatic, 409
Absorption of gases, 102 ff.; of light
Back E. M. F. in motors, 303
Balance wheel, 141
Ball bearings, 145, 146
Barometer, mercury, 30; von Guer-
Batteries, primary, 272 ff.; storage,
Bearings, ball, 145, 146; roller, 146
Becquerel, 441; portrait of, 446
Boiling points, definition of, 183;
Boyle's law, stated, 36; explained, 51
Brooklyn Bridge, 143
Calories, 152; developed by electric
Camera, pinhole, 390; photographic,
Candle power, of incandescent lamps,
Canner, steam-pressure, 184
Carburetor, 198, 199
Cartesian diver, 43
Center of gravity, 68
Chemical effects of currents, 248
Clouds, formation of, 174
Coils, magnetic properties of, 252 ff.;
Curie, 441, 442, 444; portrait of, 446
Daniell cell, 275
Davy safety lamp, 205
Densities, table of, 8, 9
Density, defined, 8; formula for, 9;
Dew, formation of, 174
Dissociation, 249, 273
Doppler effect, in sound, 326; in
Edison, 356; portrait of, 316
Electric charge, unit of, 227; distri-
Electric motor, principle of, 292;
Electrolysis of water, 248
Electrostatic voltmeter, 239
Energy, defined, 122; potential and
English equivalent of metric units, 5
Equilibrium, stable, 69; neutral, 71;
Evaporation, 53; effect of tempera-
138; of solids, 139; unequal, of
Eye, 392; pupil of, 392; nearsighted,
Faraday, 251, 290; portrait of, 290
Films, contractility of, 95; color of,
Fire syringe, 155
Force, beneath liquid, 11; definition
Franklin, 236; portrait of, 230; kite
Fraunhofer lines, 414
Freezing points, table of, 164; of
Friction, 144 ff.
Frost, formation of, 174
Fuse, electric, 269
Fusion, heat of, 161, 162
Galileo, 72, 73, 128, 132; portrait
Galvanic cell, 245
Gas engine, 191, 194
Gas meter, 46; dials of, 48
Gilbert, 225; portrait of, 222
Gram, of mass, 4; of force, 57; of