2. What sort of mirror must be used and how placed that a ruler in front of the mirror and its image may form two sides of an equilateral triangle? 3. Make a construction showing the size and position of the image formed by a concave mirror having a radius of curvature of 3 in., of an object in. long placed 4 in. in front of the mirror. 4. Make a construction showing the size and position of the image formed by a convex mirror, the object being 4 in. in front of the mirror. Use the same radius of curvature and size of object as in the last problem. 5. A candle is placed 3 ft. in front of a concave mirror having a focal length of 1 ft.; where is the image, and how large? 6. Where must an arc light be placed in front of a mirror having a radius of curvature of 6 ft. in order that its image may be focused on a screen 20 ft. from the mirror? 7. If a light is placed 2 ft. in front of a concave mirror having a radius of curvature of 6 ft., where will its image be, and how large? 8. How far must a man stand from a concave mirror having a focal length of 2 ft. in order that he may see an erect image of his face just twice its natural size? 9. Which would make the hottest image of the sun, a mirror with a focal length of 6 in. or one with 2 ft. focal length, supposing both to be of the same diameter? Why? 10. How big is the bright image formed when sunlight is reflected by a polished sphere 10 cm. in diameter and where is the image situated? Take the distance of the sun as approximately 110 times its diameter. II. What sort of mirror must be used and what must be its focal length, in order that it may form an erect image as large as an object placed 2 ft. in front of it? What kind would give an inverted image all other conditions being the same? REFRACTION. 833. Refraction.-When a beam of light passes obliquely from one medium into another, it is usually bent at the surface separating the two. This is known as refraction. It may be conveniently studied by the aid of the apparatus shown in figure 497. This consists of a circular glass vessel with flat sides and half-full of water into which a narrow beam of sunlight is directed in a darkened room. If smoke is blown into the space above the water and if the water is very slightly soapy or colored with fluorescein, the path of the beam may be distinctly traced both in the air and water. It is then observed that when the beam is sent vertically downward it is not bent, but when it is inclined it is sharply bent downward at the surface, and the bending is greater the more obliquely the beam meets the surface. The bending also takes place when light passes from water to air, as in case of the coin in the dish shown in figure 498. The coin C is out of sight of the observer's eye so long as the dish is empty, but on filling the dish with water, light coming from the coin is bent into the direction OE and comes to the eye as if from C', and the coin seems lifted into view. In the same way, because of refraction, an oar appears bent upward where it enters the water; and a tank of water, to one looking down into it, looks shallower than it really is, and the more obliquely the bottom is seen the shallower the tank appears. 834. Law of Refraction. The exact law of refraction was discovered by the Dutch physicist Snell about 1620, and may be thus stated: C FIG. 498.-Coin in dish. E When light passes from one isotropic medium into another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for light of any given wave length, whatever may be the inclination of the incident beam, and the incident, reflected, and refracted rays are all in the same plane, called the plane of incidence, which is normal to the surface. N Thus in figure 499, AD and CE are proportional to the sines of the angles i and r, respectively, and the law states that whatever may be the direction of the incident ray AO, the refracted ray OC will be so inclined that AD will be to CE in a constant ratio which depends on the nature of the two media and on the kind of light. If the upper medium is air and the lower water, AD is very nearly 80 of CE for yellow light, while in case of air and crown glass the ratio of AD to CE is more nearly for the same kind of light. 10 E M FIG. 499. 835. Index of Refraction. -This constant ratio of the sine of the angle of incidence to the sine of the angle of refraction is called the relative index of refraction of the two media concerned, and the more it differs from unity, the greater the bending of the ray in passing from one medium to the other. The relative index of refraction when light passes from air into a substance is commonly called simply the index of refraction of the substance. The absolute index of refraction of a substance is that which holds when light passes from vacuum into the substance; it differs from the ordinary index by only about one part in 3500. It may be determined by multiplying the index from air into the substance by the absolute index of refraction of air, which is 1.000292 at standard conditions. Indices of Refraction of Some Common Substances for Sodium Light 836. Cause of Refraction.—The velocity of light in water was measured by Foucault and found to be about that in air; and later Michelson found the velocity of light in bisulphide of carbon to be still less than in water. In each case it was found that the ratio of the velocity of light in air to that in the substance was equal to the index of refraction of the substance. Let us now inquire whether the assumption that a beam of light consists of a train of waves which experience a change of velocity in passing from one medium into another will account for the above result, and also whether it affords a satisfactory explanation of the law of refraction as established by experiment. In the following paragraphs we shall trace the consequences of this assumption. Air A B 837. Perpendicular Incidence: No Change in Direction.— When a beam of light in air is perpendicular to the surface of another substance, as water, in which its velocity is less, the wave fronts are parallel to the surface AB, and consequently all parts of a given wave front meet the surface AB at the same instant, and advancing into the lower medium with the same velocity everywhere, the wave front in the lower medium must remain parallel to the surface AB, and the ray direction remains unchanged. Water FIG. 500.-Perpendicular incidence of waves. The wave length, however, in the lower medium must be less than in air in the same ratio as the velocity of light in the substance is less than its velocity in air. For it must advance one wave length in the substance in the same time that it advances one wave length in air, since just as many waves per second enter the lower medium as leave the air. 838. Oblique Incidence: Change in Velocity and Direction.— If the incident beam falls obliquely on the refracting surface then the change in velocity in passing from one medium to the other causes a bending of the ray or change in direction, as shown in figure 501. For, let the heavy lines represent wave fronts one wave length apart, advancing in the direction of the arrows, and let the second medium be one, such as glass, in which the velocity is less than in air. As soon as the edge of the wave enters the glass at A it is retarded, while that part which is still in air continues to advance with the same velocity as before. Consequently the direction of the wave front is changed into the position DC. Now, BC is the distance that a wave travels in the upper medium in the same time that it travels a distance AD in the lower medium; therefore BC AD :: V: v where V is the velocity of light in the upper medium and its velocity in the lower one. Let i be the angle of in B N M E FIG. 101.-Refraction of oblique waves. cidence BCN or BAC and let r be the angle of refraction ECM or ACD, then From this it appears that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is the same as the ratio of the velocities of light in the two media, and must, therefore, be constant for all angles of incidence. 839. Adequacy of the Wave Theory.-The above interesting result is in exact agreement with the law of refraction as discovered by Snell, and it also leads to the conclusion that the relative index of refraction of two media is simply the ratio of |