Physics Part 60

5. At what distance will a 16-candle-power lamp give the same illumination as a single candle at 10 in.?

6. If the sun is at an elevation of 30 degrees what is the angle of incidence at which it strikes the surface of water? What is the angle between the incident and the reflected rays?

7. What is the difference between the phenomena of reflection of light from a white sheet of writing paper and from a piece of clear window gla.s.s?

8. A horizontal ray of light, traveling due east, strikes a vertical mirror so that after reflection it is traveling due north. If the mirror be now turned 10 degrees about a vertical axis, the north edge moving east, what will be the direction of the reflected ray?

9. The necessary illumination for reading is about 2 foot-candles. How far away may an 8-candle-power lamp be placed?

10. What is the illumination in foot-candles upon a surface 20 ft. from an arc lamp having an intensity of 1000 candle power?

11. How far from a 100-candle-power Welsbach light would the illumination be 2 foot-candles?

(3) MIRRORS AND THE FORMATION OF IMAGES

[Ill.u.s.tration: FIG. 353.--Reflection of light, (_a_) diffused, (_b_) regular.]

=362. Mirrors.=--The many purposes served by mirrors in our every-day life has made their use familiar to everyone. Yet without study and experiment few understand their properties and action. _Any smooth_ surface may serve as a mirror, as that of gla.s.s, water, polished wood, or metal. Most objects, unlike mirrors, have irregular surfaces; these scatter or diffuse the light that falls upon them. (See Fig. 353_a_.) This is called _diffused or irregular reflection_. The reflection of light from the smooth surface of a mirror is _regular_. (See Fig.

353_b_.) In every case of reflected light, however, the angle of reflection equals the angle of incidence, diffusion being due to the irregularity of the surface. It is by means of the light "diffused"

from the surface of illuminated bodies, such as plants, animals, food, and manufactured articles, that we "see" the various objects about us, and it is this light that enables us to judge of their distance, size, form, color, etc. The moon is seen by the sunlight reflected from its surface. Moonlight is therefore sunlight diffused by reflection. The _new moon_ is that phase or condition of the moon when only a narrow strip of the moon's illuminated surface is turned toward the earth. At the time of the _full moon_ the whole illuminated surface is seen.

=363. Images Formed by a Plane Mirror.=--The most common use of mirrors is in the formation of images. The way in which images are formed by a plane mirror may be ill.u.s.trated by diagrams. Thus in Fig. 354, let _L_ represent a luminous body and _E_ and _E'_ two positions of the observer's eye. Take any line or ray as _LO_ along which the light from _L_ strikes the mirror _O-O'_. It will be reflected so that angle _LOP_ equals angle _POE_. Similarly with any other ray, as _LO'_, the reflected ray _O'E'_ has a direction such as that angle _L'O'E'_ equals angle _P'O'E'_. Any other rays will be reflected in a similar manner, each of the reflected rays appearing to the eye to come from a point _L'_ behind the mirror.

[Ill.u.s.tration: FIG. 354.--The virtual image of a fixed object as seen in a plane mirror, has the same location from every position of the observer's eye.]

=364. Light Waves and Wave Diagrams.=--Just as a stick continually moved at the surface of a body of water sets up a series of waves spreading in all directions, so one may imagine a train of waves sent out by a luminous body _L_ (as in Fig. 355) to the mirror _MN_. These waves will be reflected from the mirror as if the source of light were at _L'_. It is much simpler and more convenient to locate the position of the image of a point by the use of lines or "rays" (as in Fig. 354) than by the wave diagram (as in Fig. 355). In all _ray diagrams_, however, it should be kept in mind that the _so-called_ ray is a symbol used to represent the direction taken by a part of a light wave. Thus in Fig. 354, the light from _L_ moving toward _O_ is reflected to _E_ along the line _OE_, the heavy lines representing rays.

[Ill.u.s.tration: FIG. 355.--Wave diagram of image formed in a plane mirror.]

=365. To locate the image of an object formed by a plane mirror= _requires_ simply an application of the law of reflection. Thus in Fig.

356 let _AB_ represent an object and _MN_ a plane mirror. Let _AA'_ be a ray from _A_ striking the mirror _perpendicularly_. It is therefore reflected back along the same line toward _A_. Let _AO_ represent any other ray from _A_. It will be reflected along _OE_ so that angle _r_ equals _i_. The intersection of _AC_ and _OE_ at _A'_ behind the mirror locates the image of the point _A_, as seen by reflection from the mirror. The triangles _ACO_ and _A'CO_ may be proved equal by geometry.

Therefore _A'C_ equals _AC_. This indicates that _the image of a point formed by a plane mirror is the same distance back of the mirror as the point itself is in front of it_. This principle may be used in locating the image of point _B_ at _B'_. Locating the position of the _end points_ of an image determines the position of the whole image as _A'B'_.

[Ill.u.s.tration: FIG. 356.--The image _A'B'_ is as far back of the mirror _M N_ as the object _A B_ is in front of the mirror.]

=366. How the Image is Seen.=--Suppose the eye to be placed at _E_. It will receive light from _A_ by reflection as if it came from _A'_.

Similarly light starting from _B_ reaches the eye from the direction of _B'_. There is nothing back of the mirror _in reality_ that affects our sight, the light traveling only in the s.p.a.ce in front of the mirror. Yet the action of the reflected light is such that it produces the same effect as if it came from behind the mirror. Images such as are seen in plane mirrors are called _virtual_ to distinguish them from _real_ images, in which light actually comes to the eye from the various parts of the visible image, as from the real image formed by a projecting lantern upon a screen, or by an aperture as in the pin-hole camera.

Real images therefore are those that can be obtained upon a screen while virtual images cannot.

=367. Multiple Reflection.=--If the light from an object is reflected by two or more mirrors various effects may be produced, as may be ill.u.s.trated by the _kaleidoscope_. This consists of three plane mirrors so arranged that a cross-section of the three forms an equilateral triangle. The mirrors are placed in a tube across the end of which is a compartment with a translucent cover containing pieces of colored gla.s.s.

On looking through the tube, the reflections from the several surfaces produce beautiful hexagonal designs.

[Ill.u.s.tration: FIG. 357.--Perspective view of "Pepper's ghost."]

[Ill.u.s.tration: FIG. 358.--Diagram of the "Pepper Ghost" illusion.]

=368. Optical Illusions by a Plane Mirror.=--The _illusion_ called _Pepper's Ghost_ is typical of many illusions produced by reflection. It may be ill.u.s.trated by taking a piece of plate gla.s.s, _M-N_, a tumbler of water, _W_, and a lighted candle, _C_, placed in a box, _B_, having one side open and arranged as shown in perspective in Fig. 357, and in section in Fig. 358. If the effect is produced in a darkened room, the observer at _E_ sees a virtual image of the lighted candle as if it were in the gla.s.s of water, the water being seen by transmitted light _through_ the plate gla.s.s, the latter forming a virtual image of the candle by reflection. Some of the illusions produced by this means are: (_a_) the figure suspended in mid air; (_b_) the bust of a person without a trunk; (_c_) the stage ghost; (_d_) the disappearing bouquet.

[Ill.u.s.tration: FIG. 359.--Action of a concave mirror on parallel rays of light.]

[Ill.u.s.tration: FIG. 360.--Real image formed by a concave mirror.]

=369. Concave Mirrors.=--Another useful piece of physical apparatus is the concave spherical mirror. It is frequently made from plano-convex lenses by silvering the convex surface of the lens, thus making a concave reflecting surface from the inner surface of the silvered part; they are also made by polishing the inner surfaces of metallic spherical sh.e.l.ls. The concave mirror is represented in section in Fig. 359 by the curve _MN_; _C_ is the _center of curvature_ or the center of the surface of which this mirror _MN_ is a part; the line _VC_ through the center _V_ of the mirror is called the _princ.i.p.al axis_; while any other line pa.s.sing through _C_ is called a _secondary axis_. The point midway between the vertex _V_ and center of curvature _C_ is called the _princ.i.p.al focus_, _F_. It is the point through which parallel incident rays pa.s.s after reflection. The angle _MCN_ which the curve of the mirror subtends at the center is called the aperture of the mirror. We learned in Art. 361, the angle of reflection of a ray of light is always equal to the angle of incidence no matter what the nature of the reflecting surface may be. If the reflecting surface is a regular concave surface, like the inner surface of a sphere, the rays of light coming from a point source may after reflection come to a focus, forming a real image. The two extreme points of an object should be selected for locating its image; Fig. 360 shows the construction. The real images formed by concave mirrors are always inverted. The princ.i.p.al focus of a concave mirror may be observed by holding the mirror in a beam of sunlight entering a darkened room. The sun's rays after reflection converge to form a small, round, intense spot of light, which is a real image of the sun, located at the princ.i.p.al focus of the mirror. The distance of the princ.i.p.al focus from the mirror is the least distance that a real image can be formed in front of a concave mirror.

=370. Virtual Images by Concave Mirrors.=--When light comes from a small point situated between a concave mirror and its princ.i.p.al focus, the reflected rays are divergent and hence no real image of the object can be found in front of the mirror. But if the rays are extended behind the mirror they will meet in a point called the _virtual focus_. This is the point from which they appear to come. Any image of an object situated between the princ.i.p.al focus and a concave mirror is therefore a virtual image, erect and larger than the object. (See Fig. 361.)

[Ill.u.s.tration: FIG. 361.--Virtual image formed by a concave mirror.]

=371. Construction of Real Images.=--There are five positions at which an object may be situated in front of a concave mirror, namely: (1) _beyond C_; (2) at _C_; (3) _between C and F_; (4) _at F_ and (5) _between F_ and _V_. There are two ways by means of which the image formed at each of these positions may be located, namely; (1) _experimentally_, by allowing the rays of light from a luminous body to focus on a screen and (2) _diagrammatically_. By the latter method the two rays of light are considered the course of each of which may easily be determined; first, the ray which strikes the mirror parallel to its princ.i.p.al axis and which after reflection pa.s.ses through the princ.i.p.al focus; second, the ray which pa.s.sing through the center of curvature strikes the mirror at right angles and therefore after reflection must pa.s.s directly back along its incident path. Where these two reflected rays intersect is located the real image of the object. Whenever these two rays of light do actually intersect, as in Fig. 360, a real image (_ab_) is formed of the object _AB_.

The points _A_ and _a_, _B_ and _b_ and others similarly situated on an axis extending through the center of curvature _C_ are called _conjugate foci_, for they are so related that an object being at either one, its image will be found at the other.

[Ill.u.s.tration: FIG. 362.--Action of a convex mirror upon parallel rays of light.]

=372. The Convex Mirror.=--There are few practical uses to which convex mirrors can be put. They are sometimes used to give the chauffeur of an automobile a view of the road behind him. It is then attached to the wind shield by a short rod. The reflected rays coming from a Convex mirror are always divergent (see Fig. 362), hence the image is always virtual and located behind the reflecting surface. The method of construction for images formed by a convex mirror is similar to that for concave mirrors. (See Fig. 363.) The center of curvature and princ.i.p.al focus are behind the mirror and consequently the reflected rays have to be produced backward until they meet. The images are always _virtual_, _erect_ and _smaller_ than the object.

[Ill.u.s.tration: FIG. 363.--Construction of an image by a convex mirror.]

[Ill.u.s.tration: FIG 364.--Ill.u.s.trations of Spherical Aberration.]

=373. Spherical Aberration.= Sometimes in a concave mirror when the aperture _MCN_ (Fig. 364) is large the images are blurred or indistinct.

This is due to the fact that the incident rays near the outer edge of the mirror do not focus after reflection at the same point as those which pa.s.s into the mirror near the vertex, but cross the princ.i.p.al axis at points between the mirror and princ.i.p.al focus as is shown in Fig.

364; this result is called _spherical aberration_. The larger the aperture of the mirror the more the image is blurred. Concave mirrors in practical use do not have an aperture much greater than 10 degrees. This non-focusing of the rays of light by curved reflecting surfaces may be noticed in many places, as when light is reflected from the inside of a cup that contains milk or from the inside of a wide gold ring placed on top of a piece of white paper. The pupil will note other instances.

This curve of light observed is called the _caustic by reflection_.

=374. Parabolic Mirrors.=--The best possible surface to give to concave mirrors is parabolic. This is a curve which may be generated by moving a point so that its distance from a fixed point and a fixed line are always equal. If a source of light is placed at _F_ the rays after reflection are rendered parallel. See Fig. 365. This reflector is used in automobile lamps, headlights of locomotives, search-lights, etc. It is also used in large reflecting astronomical telescopes to collect as large an amount of light as possible from distant stars and bring it to a focus. Such mirrors may be made exceedingly accurate.

[Ill.u.s.tration: FIG. 365.--Parabolic mirror.]

Important Topics

1. Reflection: regular, diffused; plane mirrors; laws of reflection.

2. Formation and location of images by plane mirrors. Wave and ray diagrams.

3. Multiple reflection, illusions.

4. Curved mirrors, uses; concave, convex, parabolic.

Exercises

1. Distinguish between regular and diffused reflection. By means of which do we see non-luminous bodies?

2. Could a perfect reflecting surface be seen? Explain.

3. A pencil is stood upright in front of a plane mirror set at an angle of 45 degrees to the vertical. Shown by a diagram the location and position of the image.