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the transmitted ray OS has totally disappeared, the whole of the light incident at 0 must be in the reflected beam. The angle of incidence IOP at which this occurs is called the critical angle. This angle for crown glass is 42.5°, for water 48.5°, for diamond 23.7°. The critical angle for any substance may be defined as the angle of incidence in that substance for which the angle of refraction into air is 90°.

We learn, then, that when a ray of light traveling in any medium meets another in which the speed is greater, it is totally reflected if the angle of incidence is greater than a certain angle called the critical angle.


1. In Fig. 382 the portion acdb of the shadow is called the umbra, aec and bdf the penumbra. What kind of source has no penumbra ? 2. The sun is much larger than the earth. Draw a diagram showing the shape of the earth's umbra and penumbra.

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


4. 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?

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

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FIG. 382. Shadow from a broad source

FIG. 383. Antiglare "lens" for automobile headlight

6. If the word "white" be painted with white paint (or whiting moistened with alcohol) across the face of a mirror and held in the path of a beam of sunlight in a darkened room, in the middle of the spot on the wall which receives the reflected beam the word "white" will appear in black letters. Explain.

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

8. 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.

9. Draw diagrams to show in what way a beam of light is bent (a) in passing through a prism; (b) in passing obliquely through a plate-glass window.

10. Explain the effect of the anti-glare "lens" (Fig. 383) upon the light of the automobile.

11. The moon has practically no atmosphere. We know this because when a star appears to pass behind the moon there is no decrease or increase in its apparent velocity while disappearing or coming into view again. If the moon had an atmosphere like the earth, explain how this would affect the apparent velocity of the star at both these times.

12. If a penny is placed in the bottom of a vessel in such a position that the edge just hides it from view (Fig. 384), it will become visible as soon as water is poured into the vessel. Explain.

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FIG. 384

FIG. 387. A diagonal eyepiece

13. A stick held in water appears bent, as shown in Fig. 385. Explain. 14. A glass prism placed in the position shown in Fig. 386 is the most perfect reflector known. Why is it better than an ordinary mirror?

15. Diagonal eyepieces containing a right-angle prism of crown glass (Fig. 387) are used on astronomical telescopes in viewing celestial objects at a high altitude. Explain.

16. Explain why a straight wire seen obliquely through a piece of glass appears broken, as in Fig. 388.

FIG. 388

17. The earth reflects sixteen times as much light to the moon as the moon does to the earth. Trace from the sun to the eye of the observer the light by which he is able to see the dark part of the new moon. Why can we not see the dark part of a third-quarter moon?


425. The corpuscular theory of light. All of the properties of light which have so far been discussed are perhaps most easily accounted for on the hypothesis that light consists of streams of very minute particles, or corpuscles, projected with the enormous velocity of 300,000 kilometers per second from all luminous bodies. The facts of straight-line propagation and reflection are exactly as we should expect them to be if this were the nature of light. The facts of refraction can also be accounted for, although somewhat less simply, on this hypothesis. As a matter of fact, this theory of the nature of light, known as the corpuscular theory, was the one most generally accepted up to about 1800.

426. The wave theory of light. A rival hypothesis, which was first completely formulated by the great Dutch physicist Huygens (1629-1695), regarded light, like sound, as a form of wave motion. This hypothesis met at the start with two very serious difficulties. In the first place, light, unlike sound, not only travels with perfect readiness through the best vacuum which can be obtained with an air pump, but it travels without any apparent difficulty through the great interstellar spaces which are probably infinitely better vacua than can be obtained by artificial means. If, therefore, light is a wave motion, it must be a wave motion of some medium which fills all space and yet does not hinder the motion of the stars and planets. Huygens assumed such a medium to exist, and called it the ether.

The second difficulty in the way of the wave theory of light was that it apparently failed to account for the fact of straight-line propagation. Sound waves, water waves, and all other forms of waves with which we are most familiar bend readily around corners, while light apparently does not. It was this difficulty chiefly which led many of the most



Great Dutch physicist, mathematician, and astronomer; discovered the rings of Saturn; made important improvements in the telescope; invented the pendulum clock (1656); developed with marvelous insight the wave theory of light; discovered in 1690 the "polarization" of light. (The fact of double refraction was discovered by Erasmus Bartholinus in 1669, but Huygens first noticed the polarization of the doubly refracted beams and offered an explanation of double refraction from the standpoint of the wave theory)



This is the largest refracting telescope in the world. The objective is an achromatic lens (see § 475) 40 inches in diameter, which is mounted in a tube 63 feet long. In order to follow the apparent motions of the heavenly bodies due to the rotation of the earth, the entire tube and counterpoises, weighing 21 tons, are driven by a giant clock. The speed of the clock is controlled by a governor, similar in principle to that of Fig. 184. By means of electric motors the telescope may be pointed in any direction. It is then clamped to the clock, which keeps it pointed toward the same region of the sky as long as may be desired. The entire floor may be raised or lowered to accommodate the observer


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