FIGURE 80.
The bending or refraction of light rays is governed by a law which holds in all cases. The bending differs with different kinds of glass, with water, with oils, or even with water mixed with chemicals; but no matter how much the bending may differ with different materials, for each material there is a fixed ratio between the angle at which the light enters and the angle at which it continues in the material. This ratio is known as the index of refraction. For water it is about 1.33; for glass about 1.5; for the diamond about 2.5; etc. This can perhaps be most easily explained by reference to Figure 80. Here the top of the shaded space represents the surface of the glass at which the light enters. The line E is drawn at right angles to this surface and the various lines, meeting in the center of the circle, represent different rays of light falling upon the glass at different angles. The heavy line shows the ray of light striking the glass and passing through it. Similarly each line is drawn differently and the nature of the lines will act as a guide by which the angle of incidence upon the glass and the angle at which the rays continue through the glass can be traced.
When it is said that glass has an index of refraction of 1.5, or 3⁄2, it means that the sine of the angle of incidence is 1.5 times as great as the sine of the angle of refraction. The sine of the angle of incidence is proportional to the length of a line drawn from the vertical E to the periphery of a circle, outside of the glass or other substance, to where it meets the ray; and the sine of the angle of refraction is proportional to the length of a line drawn from the same vertical to the periphery of the same circle, inside of the glass or other substance, where it meets the ray.
In order to lay out the path of a ray through the material, its angle of incidence being known, we may resort to the construction shown in Figure 80. Draw the incident ray at its proper angle and the vertical line at right angles to the surface of the material. From the point A, where the ray enters the circle, and at right angles to the vertical line, draw the line 1. Measure the distance from A to the vertical line and divide it by the index of refraction; and on a continuation of the line 1, lay off the distance as found. From the point so located, draw a line parallel to the vertical until it intersects the circle at the bottom. From the point at which the ray enters the medium, draw another line to where the last line drawn strikes the circle. This line will give the direction in which the ray is propagated in the medium. For glass, the index of refraction is taken as 3⁄2; hence the line 1 must contain three parts, while the continuation contains two of the same length. Upon leaving the medium, the ray is bent back again so that it continues in a direction parallel to that at which it entered, as shown in Fig. 81; and thus the case is reversed.
Figure 82 is an illustration of how both refracted and reflected rays may be several times reflected. If one will hold a match close to a mirror, looking at it somewhat from the side, there will be visible six or eight distinct reflections of it. These will be of different intensity.
If a source of light has its origin in a medium denser than air, it will be bent as shown in Figure 83. In such a case some of the rays do not leave the medium at all but are reflected back into it, as indicated at the right. The heavy line indicates what is commonly known as the critical angle. This angle varies with different substances and is the angle at which the refracted ray of light skims along the surface and does not pass out. All rays emitted at a lower angle are returned back into the medium. If an electric light were immersed in water, only the rays of light at the left of the black line would be visible to an eye outside.
FIGURE 83.
Figure 84 is an illustration of an equilateral prism. Here we have refraction on both surfaces and a light placed at A would be seen by the eye as located at B. With prisms it is easily possible to locate a light so that it may be seen in two positions at the same time.
FIGURE 84.
Figure 85 shows a double convex lens. Both sides of it are segments of circles or sections of a sphere. The center of curvature or the radius of one side is at A and that of the other at B. Each minute particle on the surface of such a part of a sphere may be looked upon as the surface of a prism, the inclination of it being indicated by a line drawn at right angles to a line passing from the point through the center of curvature. This is illustrated in the figure by the short heavy lines at right angles to the broken lines centering at A and B.
FIGURE 85.
By using the construction explained with Figure 80 and using for the left-hand surface the circle of broken lines and for the surface at E the circle of solid lines, we find the path of the ray coming from C to cross the principal optical axis at A. A similar construction for a ray at the lower side of the lens would bring it to the same point and furthermore all parallel rays would focus at this point. This point is thus known as the principal focus of the lens, and the distance between this point and the lens is called the focal length of the lens. Every lens has two principal foci, one on either side and at equal distances from the lens.
FIGURE 86.
FIGURE 87.
If, instead of subjecting the lens to parallel rays, we use rays emanating from a central point on the optical axis, they will come to a focus at some different point on the other side of the lens, as illustrated in Figure 86. If the light be placed at the principal focus of the lens, the rays leaving the lens will be parallel. If the light be brought nearer the lens, the rays leaving it will spread out as shown in Figure 87; they will leave the lens in a direction such as to make upon an observer from in front the impression that they are coming from the point C behind the lens. If the light be placed beyond the principal focus of the lens, the rays will converge to a point some distance ahead of it. This distance varies with the position of the light and the two points (light on one side and focus on the other) are known as conjugate foci of the lens.
FIGURE 88.
If an object be projected through a lens as, for instance, the arrow at the right of Figure 88, it will appear upon a screen placed on the opposite side, but will be inverted. The reason for this is that the rays of light striking the lens from the top of the arrow will be refracted as shown, cross the focal point F, and meet those which come from the same point and pass through the center of the lens in a straight line; and thus the image of the arrow head will appear at the bottom; in a similar manner the image of the tail of the arrow will appear at the top. The flatter the lens, the farther away will be the point at which the image is formed.
FIGURE 89.
If such a lens be placed over an object, the light will come to the eye as shown in Figure 89. The solid lines show the rays by which the eye receives the light and the broken lines show the direction from which it appears to come. Thus we see the object much enlarged. A lens used in this manner is spoken of as a reading glass, and the greater the curvature, the greater its magnifying power.
FIGURE 90.
FIGURE 91.
In Figure 90 is illustrated a double concave lens. Parallel rays entering this lens are scattered by it, as shown. Therefore, if such a lens be placed over an object, the light from the extremity of the object will come to the eye as indicated in Figure 91, but will give the appearance of coming along the lines H and I. Thus the object will be seen much reduced in size. Such lenses are sometimes used by artists to bring landscapes to a reduced size so that they may be viewed as a whole more easily.
FIGURE 92.
The general forms of lenses are shown in Figure 92,
In most optical instruments, lenses are used for the purpose of gathering a large number of rays of light and altering the apparent direction of the rays so that an enlarged picture may be presented to the eye. In order to accomplish this, it is necessary that the rays of light be bent or refracted. This refraction, we have already seen, is always accompanied by a dispersion which causes the light to be dissolved into its original colors more or less. This has been illustrated by means of prisms.
Wherever a single lens is used, the light around the edges of the illuminated space is always more or less colored, varying with the illuminant used. Such coloring is most noticeable along the edges of projected pictures but it also exists, though to a less noticeable degree, over the whole field, showing least in the center.
The light which is thus refracted and dispersed by one prism may be gathered again by another, as shown in Figure 93, but the light rays after passing through the second prism will be exactly parallel to the ray striking the first. The light coming out of the second prism will appear white but it will be impossible either to enlarge or diminish the size of a picture in this way; hence lenses, corrected to give white light in this manner, would be of no use.
Fortunately it has been found that, with different kinds of glass, the ratio of refraction to dispersion is different; and by combining two pieces of glass of different nature, it is possible to recombine the colors without causing the emergent ray to become parallel to the incident ray. Consider, for instance, Figure 94 in which we have drawn a prism made up of two different kinds of glass. If the right half were of a glass having the same index of refraction as the left, for the red rays for instance, these would continue through both in a straight line. If the dispersion were less in the right half, i.e., if the violet rays were refracted less—sufficiently less to cause them to approach the red—they would meet the latter at some point outside of the prism and combine into white light again, thus eliminating the colors ordinarily visible through single glass lenses.
FIGURE 95.
Whenever it is necessary to project especially good pictures upon a screen, lenses corrected in some such manner as outlined above are always used and the lenses are often combined as shown in Figure 95. In this figure, R indicates the line, through the principal axis, at which the red rays refracted by lens 1 alone would strike; and V, the line where the violet rays would be projected. The addition of lens 2 brings the red and violet together again at W. A combination of two such lenses, placed the proper distance apart and the surfaces properly proportioned, may be made to combine any two of the colors of the spectrum. Hence even with these corrected lenses there is always some coloring on the screen although it is hardly noticeable.
Figures 96, 97, and 98 are drawings showing the manner in which objective lenses are usually made up. The types at the right and left are used for camera work, while the one shown in the center is used mostly for moving picture and stereopticon projection. The end having the separate lenses is turned towards the light. Those shown in contact are glued together by the use of Canadian balsam.
FIGURE 99.
The optical system of the ordinary telescope is shown in Figure 99. Light from the distant object A is gathered by the large lens B and an image is formed as indicated by the small arrow. This image acts as the object to lens C and is projected to lens D where the rays of light are strongly refracted, entering the eye by angles which cause an enlarged view of the object at E, as indicated. There must of course be some means by which the lenses may be adjusted to each other for focusing.
FIGURE 100.
The arrangement of the opera glass in Figure 100 is quite different from the above because of the reduced size of the instrument and for the reason that an erect picture is desired, whereas the telescope above gives an inverted one. The principal difference between the two is in the eyepiece. In the opera glass this is a concave lens while in the other it is a convex lens. In this case it is necessary to have the eye very close to the lens to catch the rays of light. The opera glass, as well as the telescope, must be provided with means of varying the distance between the lenses according to the distance of the object viewed, for the purpose of focusing. In some telescopes and also opera glasses, prisms are used for the purpose of obtaining erect images. Figure 101 will show how the rays of light entering a prism are reflected and the image reversed thereby.
FIGURE 101.
Figure 102 is an explanation of the reflecting stereoscope. Let the black circles represent the eyes of the observer and let M represent two mirrors placed as shown. If two pictures taken by a stereoscopic camera are placed as indicated by the arrows at the right and the left, they will appear superimposed in the position of the arrow in the rear.
The refracting stereoscope is the one mostly used and the plan of it is shown in Figure 103. Pictures for use with stereoscopes are taken by special cameras provided with two lenses placed about as far apart as the human eyes and mounted together. Stereoscopic effects may, however, be produced even without this precaution and it is possible to obtain some queer results by combining certain pictures.
In the so-called “Camera Lucida”, prisms of the type shown in Figures 104 and 105 are used. At the left is a combination lens and reflecting prism which gives an erect image, and Figure 105 is a prism also designed to give erect images. Such instruments are used for sketching. They may be made to throw an image upon a small screen where its lines may be traced out by the artist.
The most important optical instrument with which we have to deal is the projecting arc lamp and its optical system. The passage of light through this system of lenses is altogether different from that passing through a camera lens for instance. In a camera lens the picture is formed upon the ground glass screen by the light reflected from the object. From any single point of the object, rays of light strike all parts of the lens, pass through it, and are recombined or focused at some point behind it. Under these conditions, focus can be obtained only at a certain distance behind the lens, this distance varying with the distance of the object whose light is being received by the lens.
FIGURE 106.
With our projecting lens we have no reflected light leaving the object in all directions, but instead we have rays of light having definite directions. This can be seen from Figure 106. The light used must come from a point source, the smaller and the more intense it is the better. This light is gathered by condensers, as shown at C, which are so arranged as to focus the light in the center of the objective lens D. In the moving-picture machine the light, before reaching the objective lens, is passed through the film as indicated, the arrows representing sections of film. The picture projected in this manner can be made to appear upon a screen in front of the object lenses at any distance, but the farther away it is, the larger it will be and the less bright the illumination of it. A picture projected in this manner is always inverted, and, in order to have it appear right side up, it must be placed in position upside down. Figures 107 and 108 show arrangement of lenses frequently used as condensers.
FIGURE 112.
The eye is easily deceived and is also very inaccurate in its judgment. In Figures 109 to 111, all of the lines are of precisely the same length, yet they appear to differ considerably. The reason for this error in the estimation of objects is not known. It is especially noticeable with such objects as a high hat; almost any one will estimate the height of a silk hat as much greater than it really is. In general, white objects also appear to be much larger than black objects. This can be seen by the two inscribed squares one black and the other white in Figure 112; both of these are of exactly the same size. Probably the fact that more light reaches the eye from a light-colored object than from a dark-colored one of equal proportions causes the impression of greater size.
That the mind has the power of mixing contradictory or conflicting impressions made upon it is proved by many facts. If a star, Figure 113, be pinned to the center of a wheel and rapidly revolved, the center of it will appear jet black; while the outer portions, made up of the points and the white background, will appear grey which will gradually fade to a lighter shade from the center black spot outward.
If a card be provided with a picture of a bird on one side and a ring on the other, Figure 114, and this be rapidly spun on one corner, after the manner of a top, the bird will appear to be in the center of the ring. This effect is due to the persistence of vision; an image formed upon the retina requires some time before it can be eliminated so that both images appear together.
This persistence of vision and the power of suggestion are made use of in a well-known act which consists of apparently throwing something, for instance a guinea pig, into the air and causing it to vanish. To perform this trick, the operator holds the pig in his hand and makes a few motions suggestive of tossing it into the air. Then, with a final more extreme motion on the downward swing of his hand, he drops the pig and swiftly moves his empty hand upward. Due to the persistence of vision, the audience actually still sees the pig and due to the suggestion of tossing the eyes look upward, and thus the persistence of vision and the power of suggestion create the illusion.
FIGURE 115.
Dissolving Views of Living Pictures.—This act requires a large glass plate of good clear quality arranged upon the stage, as shown in Figure 115. One of the poses is arranged as at the black circle behind the glass and when illuminated is seen by the audience. The other is arranged at one side. The lighting of both is connected to the same dimmers in such a manner that when the light of one is increasing, that of the other is diminishing. Thus the two figures are dissolved into one another. The paths of the various rays of light to different parts of the auditorium are shown in the drawing and it is possible to procure perfect registry.
Human Figure Floating or Performing in Air.—This act is arranged by means of a large mirror placed upon the stage as shown in Figure 116. In the pit out of sight of the audience is a revolving table draped in dull black and all of the pit is draped in the same manner. A figure lying upon this table dressed in light clothes will appear erect in the mirror as indicated by the arrow. If now the table is revolved, the figure will be seen as turning over in the mirror. The figure upon the table may perform a number of evolutions suggestive of floating, flying, etc. The black cloth of the pit will reflect no light and only the figure will be visible. If a glass plate is used instead of a mirror, suitable scenery may be arranged back of it. The figure must of course be brightly illuminated. By moving the table upon which the figure rests across the pit, the figure will appear to move along.
FIGURE 116.
Head Suspended in Air.—This act is worked out in bright light. It requires a mirror with a hole in the center of it large enough to admit the head of a person, as shown in Figure 117. Above the mirror suitable decorations are provided which cause one looking at the mirror to imagine seeing the back wall of a room. The ceiling must of course be kept out of view as much as possible. A person looking on sees the head and the mirror gives him the impression of vacant space about it. The head must be surrounded by a collar or drapery of some kind so that no reflection of it will be visible.
FIGURE 117.
FIGURE 118.
Magic Cabinet.—In this act a person enters the cabinet, Figure 118. The outer doors are closed for an instant and then opened. The person has disappeared! The disappearance is brought about by pulling the two mirrors, arranged inside of the cabinet, into the position indicated by the dotted lines. When the cabinet is open for inspection, these are swung to the side and are invisible. The backs are of the same design as the rest of the interior cabinet. When they are pulled together and hide the person behind them, they reflect the side walls of the cabinet and are not noticed. If the cabinet is well made and the act skilfully performed, the outer doors may even be omitted.
Head Resting on Table.—For this act a hole large enough to allow a person’s head to project through is cut in the top of a table, Figure 119. This table has only two legs and is fitted up with mirrors, as indicated by shading. The reflection of the two legs in the mirror causes the observer to see four and imagine that the space below the table is vacant.
FIGURE 119.
Multiplication of Images.—If three large mirrors be arranged in the form of an equilateral triangle, as indicated in Figure 120, a person standing in the center will see his image reflected so many times that he will receive the impression of being in the midst of a crowd. He will see the reflections of reflections repeated until by absorption so much light is lost that they finally become invisible.
FIGURE 120.
FIGURE 121.
Trick Mirror.—Rather startling effects can be produced by a thinly coated mirror A, Figure 121, behind which an electric light is arranged so that it may be easily turned on. The space behind the mirror being dark, no one suspects that it is anything but a common looking glass. It is, however, quite transparent when the light behind it is turned on. The person in front viewing himself may thus suddenly be brought to see anything that is behind the mirror. If another set of mirrors is arranged, as shown by shaded lines, the person in front of the mirror may suddenly be made to see a head floating in the air in front of him.
FIGURE 122.
The manner in which one can see through a brick is illustrated in Figure 122. Four mirrors reflect the light around it. If the mirrors are properly arranged, the person will imagine he is looking through the brick.
FIGURE 123.
The face of a person may be thrown upon a screen among clouds or other pictures in the manner shown in Figure 123. The face occupies the space marked by a half circle and two arc lamps with condensers are trained upon it at very close range. The face itself acts as a reflector projecting itself through the object lens in the center. This act is very trying on the person whose face is reflected.
At a certain distance from a concave mirror, an object will be seen inverted. If the mirror be brought closer, the image will gradually go out of focus and, by bringing the mirror still closer, it will gradually come into focus again but this time erect. Properly arranged such a mirror can be made to give weird effects, for instance a skeleton, rushing at the observer; and the image will appear to step out of the mirror.
General Requirements.—In most cities it is required that theaters be built in locations which give free space for exits on two or more sides. A common requirement is that two sides adjoin public streets or alleys and one or both the other sides be provided with an open court allowing space for fire escapes and connections to street or alley. The buildings are also, as a rule, required to be of fireproof construction and divided practically into two parts by strong fire walls; one of these parts being the auditorium, that portion of the building used by the public, and the other, the stage and its belongings.
The main fire hazard of course is on the stage and every possible precaution should be taken, first to keep a fire from starting, and second, to keep it, should it start, from communicating to the auditorium. In order to protect the audience in case a fire starts doing damage on the stage, a steel and asbestos fireproof curtain is generally provided, large enough to cover the whole proscenium opening and equipped with the necessary apparatus to lower it instantly in case of necessity. In order to keep this curtain in first-class working order it is lowered at the end of every act and in the case of continuous vaudeville performances, which are not divided into acts, at least once or twice during each performance.
This curtain must be strong enough to withstand the strain of air pressure which would exist in case of a fire raging behind it. This strain, when one considers the quantity of oil-painted scenery carried by many of the large shows, is apt to be considerable, in case of fire.
In order further to protect the audience, a large vent flue is required above the stage. The purpose of this vent is to carry off the smoke and gases. The Chicago law requires the vent to be equal in area to one-twentieth of the area of the stage and to extend fifteen feet above the highest point of the roof.
The hazard to the audience is not so much that of the actual fire, as of the rapid consumption of oxygen by the flames. This causes strangling. In the case of the Iroquois Theater fire the death of many was due almost entirely to this cause. The flames spreading rapidly consumed all of the oxygen in the tightly closed theater; at the same time the smoke and gases were spreading and hundreds of the audience inhaled this heated and vitiated air with almost instantly fatal results.
As a further precaution against fire, it is now required in all large cities, that all scenery be fireproofed to such an extent that it will not carry fire. The usual test for this is, to hold a match to a part of the cloth long enough to burn a hole through it. The fire must go out as soon as the match is withdrawn.
The following are extracts from the Chicago ordinances governing theaters of the larger class:
The building must be of fireproof construction. It must adjoin two public highways one of which may be an alley.
There must be an open space on both sides of the audience room and in front.
All balconies, galleries, main floor, and stage must connect with this open space by means of doors or fire escapes.
There must be an opening into this free space also from both sides of stage.
The floor level of the highest bank of seats on the main floor shall not be more than three feet above the sidewalk level and the lowest bank of seats not more than eight feet below this level.
All stairways must have a width of twenty inches for each one hundred seats in the room, but no stairway shall be less than four feet in width.
An iron stairway must lead from the stage to the fly floor, rigging loft, and out onto the roof.
All openings leading from the stage to the outside must be vestibuled.
Above the stage there must be a ventilating flue which must extend fifteen feet above the highest point of the roof and must equal in area one-twentieth of the area of the stage.
No seat must be less than twenty inches wide and thirty-four inches from back to back.
Every aisle must lead directly to an exit.
Between the stage and the auditorium there must be a wall of masonry and all openings in this wall must be equipped with self-closing doors.
There must be a steel curtain provided to close the main stage opening and the lowering of this curtain must be controlled at two different places.
The use of wood is allowed only for the stage floor and this must be at least two and three-fourths inches thick.
Automatic sprinklers must be provided in paint room, storeroom, property room, scene storage room, carpenter shop, and dressing rooms.
A special fire alarm system must be provided on the stage.
All scenery must be treated with a suitable fireproofing compound.
All parts of the building used by the audience must be equipped with two separate lighting systems, one of which is known as the “Emergency Lighting” and must be kept lighted at all times while the audience is in the building.
A suitable supply of axes, pike poles, and fire extinguishers must be kept on hand.
There must be regular drills of employes on the use of these appliances and in the operations of doors and vents.
All doors must swing to the outside.
FIGURE 124.
The Stage.—Figure 124 is a floor plan of a typical stage, showing the orchestra pit O, foot lights F, steel curtain C, switchboard S, stage pockets Q, proscenium side lights P, and general arrangement of scenery. The foot lights are not always curved but it seems advantageous to arrange them in this way. The rows of seats are of necessity curved so as to face each patron squarely toward the stage. If then the stage and foot lights are curved in the same way, the actors will be able to come that much closer to the audience and can thus make themselves more easily heard. The curving of the foot lights will have the further advantage of illuminating the sides of an actor more than would be the case if they were laid out in a straight line.
At each side of the steel curtain are the proscenium side lights. In some cases these lights are arranged on the audience side of the curtain, the object being to arrange them as far in front of the stage as possible. The location of these lights is awkward and it is difficult to get light from them in a useful direction.
In most theaters the switchboard is located on the right-hand side of the stage, facing the audience. This is the side from which the stage manager prefers to work and the operating electrician should be close to him. In most well-arranged theaters, the switchboard is raised above the stage level so that it may not obstruct the exits of the actors. Where practicable, the board should be let into the proscenium wall so as to allow the operator to stand as close to the proscenium opening as possible. He should have a full view of the stage at all times, since many of his cues are given by movements of the actors.
The stage pockets are laid out far enough from the center of the stage to insure their being always behind the scenery. If they are brought in too close, it is possible that, in a panorama setting, for instance, they would be visible to the audience.
Doors leading from the stage to the outside are always vestibuled in good houses. The vestibule prevents the wind from blowing the drapery about unduly and also shields the actors from unpleasant drafts.
Dressing rooms are arranged wherever the conditions of the building allow suitable space. Many of them are under the stage and others are arranged on one or both sides of the stage, sometimes very high up.
A view of the stage looking from the rear is shown in Figure 125. This figure shows the vent, the method of border light suspension, bridges for support of arc lamps or other sources of illumination, the fly floor, and the rigging loft, or “grid”.
The rigging loft is generally constructed entirely of iron slats with open spaces between them. This is necessary to insure ventilation in case of fire.