Wireless Transmission of Photographs / Second Edition, Revised and Enlarged 1919

It is also stated that by enclosing the cells in exhausted glass tubes, their inertia can be greatly reduced and their life considerably prolonged. The sensitiveness of a cell is the ratio between its resistance in the dark and its resistance when illuminated. The majority of cells have a ratio between 2:1 and 3:1, but Professor Korn has shown mathematically that by conforming to certain conditions regarding the construction the ratio of sensitiveness may be between 4:1 and 5:1. Thus a cell of R = 250,000 ohms can be reduced to 60,000 ohms from the light of a 16 c.p. lamp placed only a short distance away; the resistance may be still further decreased by continuing the illumination, but this produces a permanent defect in the cells termed "fatigue," the cells becoming very sluggish in their action and their sensitiveness gradually becoming less, the ratio between their resistance in the dark and their resistance when illuminated being reduced by as much as 30 per cent.

Excessive illumination will also produce similar results. The inertia of a cell is practically unaffected by the wavelength of the light used, but the maximum sensitiveness of a cell is towards the yellow-orange portion of the spectrum.

In addition to light, heat has also been found to vary the electrical resistance of selenium in a very remarkable manner. At 80° C. selenium is a non-conductor, but up to 210° C. the conductivity gradually increases, after which it again diminishes.

APPENDIX B

PREPARING THE METAL PRINTS

Electricians who desire to experiment in photo-telegraphy, but who have no knowledge of photography, may perhaps find the following detailed description of preparing the metal prints of some value. The would-be experimenter may feel somewhat alarmed at the amount of work entailed, but once the various operations are thoroughly grasped, and with a little patience and practice, no very great difficulty should be experienced. The simpler photographic operations, such as developing, fixing, etc., cannot be described here, and the beginner is advised to study a good text-book on the subject.

The method to be given of preparing the photographs is practically the only one available for wireless transmission, and although the manner given of preparing is perhaps not strictly professional, having been modified in order to meet the requirements of the ordinary amateur experimenter, the results obtained will be found perfectly satisfactory.

As will have been gathered from Chapter II., the camera used for copying has to have a single line screen placed a certain distance in front of the photographic plate, and the object of this screen is to break the image up into parallel bands, each band varying in width according to the density of the photograph from which it has been prepared. Thus a white portion of the photograph would consist of very narrow lines wide apart, while a dark portion would be made up of wide lines close together; a black part would appear solid and show no lines at all. It is, of course, obvious that the lines on the negative cannot be wider apart, centre to centre, than the lines of the screen. A good screen distance has been found to be 1 to 64, i.e. the diameter of the stop is ¹/₆₄th of the camera extension, and the distance of the screen lines from the photographic plate is 64 times the size of the screen opening. The following table shows what this distance is for the screen most likely to be used. The line screens used consist of glass plates upon which a number of lines are accurately ruled, the width of the lines and the spaces between being equal; the lines are filled in with an opaque substance. These ruled screens are very expensive, and are only made to order,^[10] a screen half-plate size costing from 21s. to 27s. 6d. An efficient substitute for a ruled screen can be made by taking a rather large sheet of Bristol board and ruling lines across in pure black drawing ink, the width of the lines and the spaces between being ¹/₁₂th of an inch respectively. A photograph must be taken of this card, the reduction in size determining the number of lines to the inch. A card 20 × 15 inches, with 12 lines to the inch, would, if reduced to 5 × 4 inches, make a screen having 48 lines to the inch. Preparing the board is rather a tedious operation, but the line negative produced will be found to give results almost as good as those obtained from a purchased screen.

Diameter of Stop used ¹/₆₄th of Camera Extension.

As it is impossible for many to have the use of professional apparatus designed for this particular kind of work, the fixing of the screen into an ordinary camera must be left to the ingenuity of the worker. A half-plate back focussing camera will be found suitable for general experimental work, but if this is not available, a large box camera can be pressed into service.

The writer has never seen a half-plate box camera, but one taking a 5 × 4 inch plate can be obtained second-hand very cheaply. It is a comparatively simple matter to fix the line screen into a camera of this description, the drawings Figs. 57 and 58 showing the method adopted by the writer. The two clips D, made from fairly stout brass about ¹/₂ inch wide, are bent to the shape shown (an enlarged section is given at C) and soldered at the top and bottom of one of the metal sheaths provided for holding the plates. The distance between the front of the photographic plate (the film side) and the back of the line screen (also the film side), indicated by the arrow at A, is determined by the number of lines on the screen. As will be seen from the table given, the distance for a screen having 50 lines to the inch will be ⁴¹/₆₄ths of an inch.

In all probability there will be enough clearance between the top of the sheath and the top of the camera to allow for the thickness of the clip, but if not, a shallow groove a little wider than the clip should be carefully cut in the top of the camera, so that it will slide in easily. The screen should be placed between the clips, the film side on the inside, i.e. facing the photographic plate. As with a box camera the extension is a fixture, the size of stop to be used is a fixture also. The extension of a camera (this term really applies to a bellows camera) is measured from the front of the photographic plate to the diaphragm, and if this distance in our camera is 8 inches, then the diameter of the stop to give the best results would be ¹/₆₄th of this, or ¹/₈th inch. Although for all ordinary experimental work the lens fitted to the camera will be suitable, the best type of lens for process work of all kinds is the "Anastigmat."

The picture or photograph from which it is desired to make a print should be fastened out perfectly flat upon a board with drawing pins, and if a copying stand is not available it must be placed upright in some convenient position. The diagram Fig. 59 gives the disposition of the apparatus required for copying. A simple and inexpensive copying stand is shown in Fig. 60. The blackboard A should be about 30 inches square, and must be fastened perfectly upright upon the base-board B. The stand C should be made so that it slides without any side play between the guides D, and should be of such a height that the lens of the camera comes exactly opposite the Fig. 59. L, L, lamps; A, board with picture; S, line screen; P, photographic plate. Fig. 60. centre of the board A. The camera, if of the box type, can be secured to the stand by means of a screw and wingnut, the screw being passed from the inside as shown. The beginner is advised to photograph only very bold and simple subjects, such as black and white drawings or enlargements. It is not safe to trust to the view-finders as to whether the whole of the picture is included on the plate, a piece of ground glass the same size as the plate sheaths, and used as a focussing screen, being much more reliable. It is a good plan to focus the camera for a number of different-sized pictures, marking the board A, and the guides D, so that adjustment is afterwards a very simple matter.

The make of plate used is also a great factor in getting a good negative, and Wratten Process Plates will be found excellent. As already mentioned, such subjects as the exposure and the development of the plate cannot be dealt with here, these subjects having been exhaustively treated in several text-books on photography. With an arc lamp the exposure is about twice as long as in daylight, but the exposure varies with the amount of light admitted to the plate, character of the source of light, and the sensitiveness of the plate used, etc. The writer has used acetylene gas lamps for this purpose with great success. The beginner is advised to use artificial light, as this can be kept perfectly even. With daylight, however, the light is constantly fluctuating, and this renders the use of an actinometer a necessity for correct exposure. After development, if the plate is required for immediate use, it can be quickly dried by soaking for a few minutes in methylated spirit.

Having obtained a good negative, the next operation is to prepare what is known as a metal print. For this we shall require some stout tin-foil or lead-foil, about 12 or 15 square feet to the pound, and this should be cut into pieces of such a size that it allows a lap of ³/₁₆ inch when wrapped round the drum of the transmitting machine. Obtain some good fish-glue and add a saturated solution of bichromate of potash in the proportion of 4 parts of potash to 40 or 50 parts of glue. Pour a little of this glue into a shallow dish, lay a sheet of foil upon a flat board, and with a fairly stiff brush (a flat hog's-hair as wide as possible) proceed to coat the sheet of foil with a thin but perfectly even coating of glue. The thickness of the coating can only be found by trial, for if the coating is too thick a longer time will be required for printing; but it must not be thin enough to show interference colours. After the coating has been laid on, a soft brush, such as photographers use for dusting dry plates, should be passed up and down, and across and across, with light, even strokes to remove any unevenness. A glue solution used by professional photo-engravers is as follows:

The bichromate should be dissolved in the water, and, when added to the glue, stir very thoroughly in order that complete mixing may take place. The coating may be done in a good light, not bright sunlight, but it must be dried in the dark, because, although insensitive while in a moist condition, it becomes sensitive immediately on desiccation. If allowed to dry in the light the whole coating will become insoluble, and for this reason the brushes used should be washed out as soon as they are finished with. The sheets will take about 15 minutes to dry in a perfectly dry room, but it is not advisable to prepare many sheets at once, as they will not keep for more than two or three days.

The prepared negative must now be placed in an ordinary printing frame, and a print taken off upon one of the metal sheets in the same way as a print is taken off upon ordinary sensitised paper. In daylight the exposure varies from 5 to 20 minutes, but in artificial light various trials will have to be made in order to get the best results, the exposure varying with the amount of bichromate in the coating; the proportion of the bichromate to the glue should remain about 6 per cent. Light from a 25 ampere arc lamp for 2 to 5 minutes, at a distance of 18 inches, will generally suffice to "print" the impression on the metal sheets. The printing finished, the metal print should be laid upon a sheet of glass and held under a running stream of water. The washing is complete as soon as the unexposed parts of the glue coating have been entirely washed away leaving the bare metal, and this will take anything from 3 to 7 minutes, depending upon the thickness of the film. As soon as it is dry the print is ready for use.

As already mentioned, the negative from which the metal print is made requires that the lines be perfectly sharp and opaque, and the spaces between perfectly transparent. Ordinary dry plates are too rapid, a rather slow plate being required. Wratten Process Plates give excellent results, and the following is a good developer to use with them:

This developer should be used for 6 minutes at a temperature of 50° F., 3¹/₂ minutes at 65°, and 1³/₄ minutes at 80°. It is best only used once. If an intensifier is required, the following formula will be found to give satisfactory results:

Allow to cool, completely pour off from any crystals, and add:

Allow negative to bleach thoroughly, wash well in water, and blacken in 10 per cent ammonia .880, or 5 per cent sodium sulphide.

In preparing the negatives and metal prints the following points should be observed:

A good negative should have the lines perfectly sharp and opaque; there should be no "fluff" between the lines even when they are close together.

A properly exposed and developed negative should not require any reducing or intensifying.

If the lamps used for illuminating the copying board are placed 2 feet away, and the exposure required is 5 minutes, the exposure, if the lamps are placed 4 feet away, will be 20 minutes, as the amount of light which falls upon an object decreases as the inverse square of the distance.

Get the coating on the foil as thin as possible, and err on the side of over-exposure, for if the coating is thick and has been under-exposed, excessive washing will dissolve the whole coating; for, unless insolubilisation has taken place right up to the metal base, the under parts will remain in a more or less soluble condition.

On no account must the unexposed sheets be placed near a fire, otherwise they will be spoilt, the whole coating becoming insoluble; heat acting in the same manner as light.

In washing, keep the print moving so that the stream of water does not fall continually in one place. It is best to hold the print so that the water runs off in the direction of the lines.

To dry the prints after washing they can be laid out flat in a moderately warm oven, or before a stove, the heat of course not being sufficient to cause the coating to peel.

To render the glue image more distinct the print should be immersed for a few seconds in an aniline dye solution, the glue taking up the colour readily. These dyes are soluble in either water or alcohol. A dye known as "magenta" is very good.

The process of coating the metal sheets must be performed as quickly as possible (about 10 seconds), as owing to the peculiar nature of the bichromated glue it soon sets, and once this has taken place it is impossible to smooth down any unevenness.

See that the negative and metal sheet make good contact while printing.

If the glue solution does not adhere to the surface of the foil in a perfectly even film, but assumes a streaky appearance, a little liquid ammonia, or a weak solution of nitric acid, rubbed over the surface of the foil, which is afterwards gently scoured with precipitated chalk on a tuft of cotton wool, will remove the grease which is the cause of the difficulty.

A photograph of a picture prepared from a line negative is given in Fig. 61. For a great many experiments, and in order to save time, trouble, and expense, sketches drawn upon stout lead-foil in an insulating ink will answer the purpose admirably, but if any exact work is to be done a single line print is of course absolutely necessary. The insulating ink can be prepared by dissolving shellac in methylated spirit, or ordinary gum can be used. A very fine brush should be used in place of a pen, as the gum will not flow freely from an ordinary nib unless greater pressure than the foil will safely stand be applied. A sketch prepared in this manner is shown in Fig. 62. A little aniline dye should be added to the gum to render it more visible, or a mixture of gum and liquid indian ink will be found suitable.

With the copying arrangement already described it is only possible to employ it for reducing, it being necessary to employ a bellows camera with a back focussing attachment for purposes of enlarging, and this constitutes the chief drawback to the use of a fixed focus camera. By replacing the box camera with a focussing camera of the same size, we shall have a piece of apparatus capable of reducing or enlarging, only in this case the camera should be a fixture and the board, A, arranged to slide backwards and forwards instead.

An extra improvement would be to rule the surface of the copying board, A, in a manner similar to that shown in the diagram, Fig. 63. The rulings should be marked off from the centre of the board, and should enclose parallelograms of the various plate sizes ranging from 3¹/₄ × 4¹/₄ inches up to the full size of the board. By fastening the picture or photograph to be copied in the space on the board corresponding in size, we can ensure that it is in the correct position for the whole to be included on the photographic plate, providing, of course, that the centre of lens and board coincide.

With regard to the lens required, the practice adhered to by most photographers is to use a lens having a focal length equal to the diagonal of the plate used. Thus for a ¹/₄-plate camera a 5-inch lens should be used, and for a ¹/₂-plate an 8-inch lens, and so on. For a 5 × 4 inch camera a 6-inch lens will be required. The following is a simple rule for finding the conjugate foci of a lens, and is useful in obtaining the distance from the lens to the photographic plate and the picture to be copied. Let us suppose that we wish to make a 1¹/₂ times enlarged line negative from a 4¹/₄ × 3¹/₄ inch print. Add 1 to the number of times it is required to enlarge and multiply the result by the focal length of the lens in inches. In the present case this will be 1¹/₂ + 1 = 2¹/₂; and if a 6-inch lens is used, 2¹/₂ × 6 = 15 inches will be the distance of the lens from the plate. Divide this number by the number of times it is desired to enlarge, and the distance of the lens from the picture to be copied is obtained; in this instance 15 ÷ 1¹/₂ = 10 inches. The same rule can be followed when it is required to reduce any given number of times, only in this case the greater number will represent the distance between the lens and the picture to be copied, and the lesser number the distance between the lens and the plate.

In reducing, a ¹/₄-plate lens will be found to fully cover a 5 × 4 inch plate, providing the reduction is not greater than three to one.

APPENDIX C

LENSES

In this small volume it is not desirable, neither is it intended, to give an exhaustive treatment on the subject of lenses and their action, but as optics plays an important part in the transmission of photographs, both by wireless and over ordinary conductors, the following notes relating to a few necessary principles have been included as likely to prove of interest.

Light always travels in straight lines when in a medium of uniform density, such as water, air, glass, etc., but on passing from one medium to another, such as from air to water, or air to glass, the direction of the light rays is changed, or, to use the correct term, refracted. This refraction of the rays of light only takes place when the incident rays are passed obliquely; if the incident rays are perpendicular to the surface separating the two media they are not refracted, but continue their course in a straight line.

All liquid and solid bodies that are sufficiently transparent to allow light rays to pass through them possess the power of bending or refracting the rays, the degree of refraction, as already explained, depending upon the nature of the body.

The law relating to refraction will perhaps be better understood by means of the following diagram. In Fig. 64 let the line AB represent the surface of a vessel of water. The line CD, which is perpendicular to the surface of the water, is termed the normal, and a ray of light passed in this direction will continue in a straight line to the point E. If, however, the ray is passed in an oblique direction, such as ND, it will be seen that the ray is bent or refracted in the direction DM; if the ray of light is passed in any other oblique direction, such as JD, the refracted ray will be in the direction DK. The angle NDC is called the angle of incidence and MDE the angle of refraction. If we measure accurately the line NC, we shall find that it is 1¹/₃, or more exactly 1.336, times greater than the line EM. If we repeat this measurement with the lines JH and PK we shall find that the line JH also bears the proportion of 1.336 to the line PK. The line NC is called the sine of the angle of incidence NDC, and EM the sine of the angle of refraction MDE.

Therefore in water the sine of the angle of incidence is to the sine of the angle of refraction as 1.336 is to 1, and this is true whatever the position of the incident ray with respect to the surface of the water. From this we say that the sines of the angles of incidence and refraction have a constant proportion or ratio to one another.

The number 1.336 is termed the refractive index, or coefficient, or the refractive power of water. The refractive power varies, however, with other fluids and solids, and a complete table will be found in any good work on optics.

Glass is the substance most commonly used for refracting the rays of light in optical work, the glass being worked up into different forms according to the purpose for which it is intended. Solids formed in this way are termed lenses. A lens can be defined as a transparent medium which, owing to the curvature of its surfaces, is capable of converging or diverging the rays of light passed through it. According to its curvature it is either spherical, cylindrical, elliptical, or parabolic. The lenses used in optics are always exclusively spherical, the glass used in their construction being either crown glass, which is free from lead, or flint glass, which contains lead and is more refractive than crown glass. The refractive power of crown glass is from 1.534 to 1.525, and of flint glass from 1.625 to 1.590. Spherical surfaces in combination with each other or with plane surfaces give rise to six different forms of lenses, sections of which are given in Fig. 65.

All lenses can be divided into two classes, convex or converging, or concave or diverging. In the figure, b, c, g are converging lenses, being thicker at the middle than at the borders, and d, e, f, which are thinner at the middle, being diverging lenses. The lenses e and g are also termed meniscus lenses, and a represents a prism. The line XY is the axis or normal of these lenses to which their plane surfaces are perpendicular.

Let us first of all notice the action of a ray of light when passed through a prism. The prism, Fig. 66, is represented by the triangle BBB, and the incident ray by the line TA. Where it enters the prism at A its direction is changed and it is bent or refracted towards the base of the prism, or towards the normal, this being always the case when light passes from a rare medium to a dense one, and where the light leaves the opposite face of the prism at D it is again refracted, but away from the normal in an opposite direction to the incident ray, since it is passing from a dense to a rare medium. The line DP is called the emergent or refracted ray. If the eye is placed at T, and a bright object at P, the object is seen not at P, but at the point H, since the eye cannot follow the course taken by the refracted rays. In other words, objects viewed through a prism always appear deflected towards its summit.

In considering the action of a lens we can regard any lens as being built up of a number of prisms with curved faces in contact. Such a lens is shown in Fig. 67, the light rays being refracted towards the base of the prisms or towards the normal, as already explained; while the top half of the lens will refract all the light downwards, the bottom half will act as a series of inverted prisms and refract all the light upwards.

If a beam of parallel light—such as light from the sun—be passed through a double convex lens L, Fig. 68, we shall find that the rays have been refracted from their parallel course and brought together at a point F. This point F is termed the principal focus of the lens, and its distance from the lens is known as the focal length of that lens. In a double and equally convex lens of glass the focal length is equal to the radius of the spherical surfaces of the lens. If the lens is a plano-convex the focal length is twice the radius of its spherical surfaces. If the lens is unequally convex the focal length is found by the following rule: multiply the two radii of its surfaces and divide twice that product by the sum of the two radii, and the quotient will be the focal length required. Conversely, by placing a source of light at the point F the rays will be projected in a parallel beam the same diameter as the lens. If, however, instead of being parallel, the rays proceed from a point farther from the lens than the principal focus, as at A, Fig. 69, they are termed divergent rays, but they also will be brought to a focus at the other side of the lens at the point a. If the source of light A is moved nearer to the principal focus of the lens to a point A¹ the rays will come to a focus at the point a¹, and similarly when the light is at A² the rays will come to a focus at the point a². It can be found by direct experiment that the distance fa increases in the same proportion as AF diminishes, and diminishes in the same proportion as AF increases. The relationship which exists between pairs of points in this manner is termed the conjugate foci of a lens, and though every lens has only one principal focus, yet its conjugate foci are innumerable.

The formation of an image of some distant object in its principal focus is one of the most useful properties of a convex lens, and it is this property that forms the basis of several well-known optical instruments, including the camera, telescope, microscope, etc.

If we take an oblong wooden box, AA, and substitute a sheet of ground glass, C, for one end, and drill a small pinhole, H, in the centre of the other end opposite the glass plate, we shall find that a tolerably good image of any object placed in front of the box will be formed upon the glass plate. The light rays from all points of the object, BD, Fig. 70, will pass straight through the hole H, and illuminate the ground glass screen at points immediately opposite them, forming a faint inverted image of the object BD. The purpose of the hole H is to prevent the rays from any one point of the object from falling upon any other point on the glass screen than the point immediately opposite to it, therefore the smaller we make H, the more distinct will be the image obtained. Reducing the size of H in order to produce a more distinct image has the effect of causing the image to become very faint, as the smaller the hole in H, the smaller the number of rays that can pass through from any point of the object. By enlarging the hole H gradually, the image will become more and more indistinct until such a size is reached that it disappears altogether.

If in this enlarged hole we place a double convex lens, LL, Fig. 71, whose focal length suits the length of the box, the image produced will be brighter and more distinct than that formed by the aperture, H, since the rays which proceed from any point of the object will be brought by the lens to a focus on the glass screen, forming a bright distinct image of the point from which they come. The image owes its increased distinctness to the fact that the rays from any one point of the object cannot interfere with the rays from any other point, and its increased brightness to the great number of rays that are collected by the lens from each point of the object and focussed in the corresponding point of the image. It will be evident from a study of Fig. 71 that the image formed by a convex lens must necessarily be inverted, since it is impossible for the rays from the end, M, of the object to be carried by refraction to the upper end of the image at n. The relative positions of the object and image when placed at different distances from the lens are exactly the same as the conjugate foci of light rays as shown in Fig. 69.

The length of the image formed by a convex lens is to the length of the object as the distance of the image is to the distance of the object from the lens. For example, if a lens having a focal length of 12 inches is placed at a distance of 1000 feet from some object, then the size of the image will be to that of the object as 12 inches to 1000 feet, or 1000 times smaller than the object; and if the length of the object is 500 inches, then the length of the image will be the ¹/₁₀₀₀th part of 500 inches, or ¹/₂ inch.

The image formed by the convex lens in Fig. 71 is known as a real image, but in addition convex lenses possess the property of forming what are termed virtual images. The distinction can be expressed by saying, real images are those formed by the refracted rays themselves, and virtual images those formed by their prolongations. While a real image formed by a convex lens is always inverted and smaller than the object, the virtual image is always erect and larger than the object. The power possessed by convex lenses of forming virtual images is made use of in that useful but common piece of apparatus known as a reading or magnifying glass, by which objects placed within its focus are made larger or magnified when viewed through it; but in order to properly understand how objects seem to be brought nearer and apparently increased in size, we must first of all understand what is meant by the expression, the apparent magnitude of objects.

The apparent magnitude of an object depends upon the angle which it subtends to the eye of the observer. The image at A, Fig. 72, presents a smaller angle to the eye than the angle presented by the object when moved to B, and the image therefore appears smaller. When the object is moved to either B or C, it is viewed under a much greater angle, causing the image to appear much larger. If we take a watch or other small circular object and place it at A, which we will suppose is a distance of 50 yards, we shall find that it will be only visible as a circular object, and its apparent magnitude or the angle under which it is viewed is then stated to be very small. If the object is now moved to the point B, which is only 5 feet from the eye, its apparent magnitude will be found to have increased to such an extent that we can distinguish not only its shape, but also some of the marking. When moved to within a few inches from the eye as at C, we see it under an angle so great that all the detail can be distinctly seen. By having brought the object nearer the eye, thus rendering all its parts clearly visible, we have actually magnified it, or made it appear larger, although its actual size remains exactly the same. When the distance between the object and the observer is known, the apparent magnitude of the object varies inversely as the distance from the observer.

Let us suppose that we wish to produce an image of a tree situated at a distance of 5000 feet. At this distance the light rays from the tree will be nearly parallel, so that if a lens having a focal length of 5 feet is fastened in any convenient manner in the wall of a darkened room the image will be formed 5 feet behind the lens at its principal focus. If a screen of white cardboard be placed at this point we shall find that a small but inverted image of the tree will be focussed upon it. As the distance of the object is 5000 feet, and as the size of the received image is in proportion to this distance divided by the focal length of the lens, the image will be as 5000 ÷ 5, or 1000 times smaller than the object.

If now the eye is placed six inches behind the screen and the screen removed, so that we can view the small image distinctly in the air, we shall see it with an apparent magnitude as much greater than if the same small image were equally far off with the tree, as 6 inches is to 5000 feet, that is 10,000 times. Thus we see that although the image produced on the screen is 1000 times less than the tree from one cause, yet on account of it being brought near to the eye it is 10,000 times greater in apparent magnitude; therefore its apparent magnitude is increased as 10,000 ÷ 1000, or 10 times. This means that by means of the lens it has actually been magnified 10 times. This magnifying power of a lens is always equal to the focal length divided by the distance at which we see small objects most distinctly, viz. 6 inches, and in the present instance is 60 ÷ 6, or 10 times.

When the image is received upon a screen the apparatus is called a camera obscura, but when the eye is used and sees the inverted image in the air, then the apparatus is termed a telescope.

The image formed by a convex lens can be regarded as a new object, and if a second lens is placed behind it a second image will be formed in the same manner as if the first image were a real object. A succession of images can thus be formed by convex lenses, the last image being always treated as a fresh object, and being always an inverted image of the one before. From this it will be evident that additional magnifying power can be given to our telescope with one lens by bringing the image nearer the eye, and this is accomplished by placing a short focus lens between the image and the eye. By using a lens having a focal length of 1 inch, and such a lens will magnify 6 times, the total magnifying power of the two lenses will be 10 × 6 = 60 times, or 10 times by the first lens and 6 times by the second. Such an instrument is known as a compound or astronomical telescope, and the first lens is called the object glass and the second lens the magnifying glass, or eye-piece.

We are now in a position to understand how virtual images are formed, and the formation of a virtual image by means of a convex lens will be readily followed from a study of Fig. 73. Let L represent a double convex lens, with an object, AB, placed between it and the point F, which is the principal focus of the lens. The rays from the object AB are refracted on passing through the lens, and again refracted on leaving the lens, so that an image of the object is formed at the eye, N. As it is impossible for the eye to follow the bent rays from the object, a virtual image is formed and is seen at A¹B¹, and is really a continuation of the emergent rays. The magnifying power of such a lens may be found by dividing 6 inches by the focal length of the lens, 6 inches being the distance at which we see small objects most distinctly. A lens having a focal length of ¹/₄ inch would magnify 24 times, and one with a focal length of ¹/₁₀₀th of an inch 600 times, and so on. The magnifying power is greater as the lens is more convex and the object near to the principal focus. When a single lens is applied in this manner it is termed a single microscope, but when more than one lens is employed in order to increase the magnifying power, as in the telescope, then the apparatus is termed a compound microscope.

Unlike a convex lens, which can form both real and virtual images, a concave lens can only produce a virtual image; and while the convex lens forms an image larger than the object, the concave lens forms an image smaller than the object. Let L, Fig. 74, represent a double concave lens, and AB the object. The rays from AB on passing through the lens are refracted, and they diverge in the direction RRRR, as if they proceeded from the point F, which is the principal focus of the lens, and the prolongations of these divergent rays produce a virtual image, erect and smaller than the object, at A¹B¹. The principal focal distance of concave lenses is found by exactly the same rule as that given for convex lenses.