4. Show by diagrams the position and location of the images of a pencil (a) when standing erect and in front of a _vertical_ mirror. (b) when standing upon a horizontal mirror.
5. What is the difference between a real and a virtual image?
6. A standard candle and a lamp give equal illuminations to a screen that is 1 ft. from the candle and 6 ft. from the lamp. What is the candle power of the lamp? Explain.
7. Why are walls finished in rough plaster or painted with soft tones without gloss better for schoolrooms than glossy paints or smooth white plaster?
8. Try to read a printed page by looking at its image in a mirror. write your name backward on a sheet of paper, and then look at the image of the writing in a mirror. What effect is produced by the mirror in each case?
9. If the point of a pencil is held to the surface of a piece of plate-gla.s.s mirror two or more images may be seen in the mirror.
Explain.
10. Given a small lighted candle, a concave mirror, a meter stick, and a white screen, how would you prove the statements made in Arts. 369 and 370 concerning the location of images formed by concave mirrors? Make the diagram in each case.
11. Why do images seen in a quiet pond of water appear inverted? Explain by a diagram.
(4) REFRACTION OF LIGHT
=375. Common Examples of Refraction.=--Everyone has noticed the apparent bending of an oar, of a stick, or of a spoon when placed in water (see Fig. 366), while many have observed that the bottom of a pond or stream looks nearer to the surface than it really is. These and similar illusions are due to the _refraction_ or bending of light rays as they pa.s.s from one medium to another. The principles of refraction are among the most useful found in the study of light since application is made of them in the construction and use of important optical instruments, such as the camera, microscope, telescope, and the eye.
[Ill.u.s.tration: FIG. 366.--The stick appears to be bent on account of refraction.]
=376. Action of Light Undergoing Refraction.=--If a beam of sunlight be admitted to a darkened room and reflected by a mirror so that it strikes the surface of water in a gla.s.s jar, a part of the beam may be seen to be reflected while another portion is transmitted through the water (Fig. 367). The reflected beam follows the law of reflection while the transmitted beam is seen to be _refracted_, or to have its courses slightly changed in direction upon entering the water. If the mirror is turned so that the angle at which the light strikes the water is changed, the amount of refraction or change of course of the light is varied. When the light strikes the water perpendicularly there is no refraction. On the other hand, the greater the angle at which the light strikes the water the greater the bending.
[Ill.u.s.tration: FIG. 367.--Part of the ray is reflected and part pa.s.ses into the water and is refracted.]
[Ill.u.s.tration: FIG. 368.--Ill.u.s.trating the laws of refraction of light.]
=377. Laws of Refraction.= The action of light on entering, pa.s.sing through, and leaving a great variety of substances has been carefully studied. A summary of the results of these observations is given in the following _laws of refraction_: I. _When light enters a transparent body, perpendicularly, it pa.s.ses on without changing its direction._ II. _When light enters a denser transparent body obliquely, it is bent toward the perpendicular; when light enters a less dense body obliquely, it is bent away from the perpendicular._ (See Fig. 368.)
=378. The cause of refraction= may be ill.u.s.trated by considering a line of men moving across a field and occupying at equal time intervals the successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that the upper and lower parts of the field have a smooth hard surface, while at the center is a strip of newly ploughed ground. The line will move more slowly over the ploughed field than over the hard field. This will result in a r.e.t.a.r.dation of the end of the line first striking the soft ground with a resulting change of direction of the line, _toward_ the perpendicular to the edge of the field (_on entering the place of more difficult travel_), and _away_ from the perpendicular on moving into a place where _increased speed results_.
[Ill.u.s.tration: FIG. 369.--Diagram ill.u.s.trating the cause of refraction.]
=379. Index of Refraction.=--By studying the change of direction of the marching men as shown in Fig. 369 it is evident _first_ that it is due to a difference in speed in the two media. It is not easy to measure the speed of light in a medium. However, the amount of refraction may be determined easily and from this the _relative_ speed may be computed.
The _number that expresses the ratio of the speed of light in air to its speed in another medium is called the index of refraction of that medium_. The relative speeds of light, or the indices of refraction for some substances, are: water, 1.33, crown gla.s.s, 1.51, flint gla.s.s, 1.61, diamond, 2.47, carbon bisulphide, 1.64.
[Ill.u.s.tration: FIG. 370.--The incident ray and the emergent rays are parallel.]
=380. Plates, Prisms, Lenses.=--The refraction of light is usually observed when it is pa.s.sing through a plate, a prism, or a lens. The important differences between the effects of each in refracting light are ill.u.s.trated in Figs. 370, 371 and 372. In Fig. 370 it is seen that the refraction of the ray on entering the gla.s.s is counteracted by the refraction away from the perpendicular upon leaving it. So that the entering and emergent rays are _parallel_. In Fig. 371 the refraction at the two surfaces of the prism results in a change of direction of the ray, the course being bent toward the _thicker_ part of the _prism_. In Fig. 372 it may be noticed that the convex lens resembles two prisms with their bases together. Since all parts of the lens refract light toward the thicker part, the center, the effect of the convex lens is to bring the rays of light to a focus, at _F_.
[Ill.u.s.tration: FIG. 371.--Effect of a prism upon a ray of light.]
[Ill.u.s.tration: FIG. 372.--The convex lens brings the rays of light to a focus.]
=381. Total Reflection.=--It has been shown that when light pa.s.ses from a _denser to a lighter_ medium, as from gla.s.s or water to air, that the beam is refracted _away_ from the perpendicular. This is ill.u.s.trated in Fig. 373. The diagram represents the change in the course of a ray of light that pa.s.ses through water to a surface with air above it. A ray striking perpendicularly pa.s.ses through without refraction. Other rays show increasing refraction with increasing angle of incidence. For one ray the angle of refraction is so large that the refracted ray is parallel to the surface. When this condition is reached, the _angle of incidence_ is called the _critical angle_. Any increase in the angle of incidence causes all of the light to be reflected as is the beam _E_.
This action is called _total reflection_, the course of the reflected ray being according to the law of reflection. _A right-angle prism_ (see Fig. 374) is often used where a mirror would ordinarily be employed, the total reflection occurring within the prism giving more satisfactory results than a mirror. See Art. 398 for a description of the Zeiss binocular field-gla.s.s for an example of this use of total reflection.
[Ill.u.s.tration: FIG. 373.--An example of total reflection.]
[Ill.u.s.tration: FIG. 374.--Total reflection in a right-angle prism.]
The mirage (see Fig. 375) is an optical illusion by which distant objects, below the horizon, are sometimes plainly seen. This phenomenon is most frequently observed in hot, desert regions, when the air conditions are such that the lower strata near the ground are very much hotter than those above. These lower strata, having expanded the most, are less dense than the cooler ones above. Hence a ray of light traveling obliquely downward is refracted more and more until total reflection takes place. The images seen are inverted giving a representation of trees or other objects reflected on the surface of still water. The mirage is also frequently seen at sea, ships being observed, sometimes erect, sometimes inverted, apparently sailing in the clouds near the horizon. Over the Great Lakes, trees, boats, and towns on the opposite sh.o.r.e, sixty or seventy miles away, can sometimes be plainly seen, apparently but a few miles out. In this case the images are erect, the total reflection being from warm, still layers of air over colder layers near the water.
[Ill.u.s.tration: FIG. 375.--Diagram of a mirage.]
Important Topics
(A) Refraction: cause, ill.u.s.tration, two principles.
(B) Index of refraction, meaning.
(C) Plates, prisms, lenses, action of each.
(D) Total reflection, uses.
Exercises
1. Compute the speed of light in water, the index of refraction being 1.33.
2. If one wished to shoot a fish under water, should he aim at the apparent location of the fish as viewed from the air? Explain, using a diagram.
3. Define refraction. Mention two ill.u.s.trations of this action that you have observed out of school.
4. Why does the moon look larger near the horizon?
5. Is your reflection seen in a pool of water upside down? Why?
6. Why does it whiten mola.s.ses candy to pull it?
7. When looking at a building through the ordinary gla.s.s of a window why do straight lines of the building appear to be so distorted? What makes them appear to move as you move your head slightly?
8. Explain the phenomenon which one observes when looking at an object through the air arising from a hot stove or radiator.
9. Frequently the horizontal diameter of the setting sun appears to be greater than the vertical. Explain.
10. Explain why one observes several images of a luminous body like a lighted candle when the reflected light from a thick gla.s.s mirror enters the eye, the angle of reflection being large.
(5) THE FORMATION OF IMAGES BY LENSES
=382. Uses of Lenses in Optical Instruments.=--The use of instruments that employ lenses in their operation, such as spectacles, reading and opera gla.s.ses, and the camera, microscope, and telescope, is familiar to most students of physics. The part played by the lenses, however, is not generally understood. Consequently the study of the formation of images by lenses is of general interest and importance.
=383. Forms of Lenses.=--While a lens may be formed from any transparent solid it is commonly made of gla.s.s. It may have two curved surfaces or one curved and one plane surface. Most lenses are _spherical lenses_, since their curved surfaces form a part of the surface of a sphere. Fig.
376 represents a spherical lens with a curved surface coinciding with that of a sphere whose center is at _C_. This center is called the _center of curvature_, while the radius of the sphere _R_, is the _radius of curvature_.