PERISCOPE, an optical instrument used in land warfare and in submarine navigation to enable an observer to see his sur roundings while remaining under cover or submerged. It invari ably includes among its optical elements two mirrors or reflecting prisms to change the direction in which the light travels, the first to divert it down the interior of a tube and the second to guide it into a direction convenient for observation. In addition there is usually a more or less complex telescopic system, and in some types devices are added for taking ranges, for measuring the speeds with which various objects are moving, for searching the whole sky, and for varying the magnifying power of the tele scope.
The simplest type of periscope, consisting of a tube and two mirrors at its ends placed parallel to one another and at an angle of 45° with the axis of the tube, is not of recent origin, but the great developments which have been made in modern times are due to requirements for submarine navigation. These develop ments secure a large angular field of view when the tube is of con siderable length and yet of restricted diameter and give an en larged image. As in other military instruments, clear vision through the periscope even under adverse conditions is of great importance, and the beam of light brought to the observer's eye must therefore be of a diameter large enough to fill his pupil when it is somewhat widely opened. These various conditions tend to be opposed to one another, so that the design of each instrument represents a compromise which may vary over a considerable range as more or less importance is attached to one or the other of these requirements.
A typical submarine periscope consists externally of a tube about 3o ft. long and 6 in. in diameter except for a length of from two to three feet at the top, where the diameter may be reduced to two inches or even less. At the lower end a length of several feet of the full diameter is required for passing through the long stuffing box where the instrument enters the hull of the sub marine. A diameter of about six inches is needed to resist the bending moment caused by the resistance of the water as the submarine advances ; an increase in the diameter adds to the re sistance offered by the periscope to the boat's progress. The narrowing at the top is introduced to make the part which pro jects above the surface of the water less conspicuous. The optical
effects of this constricted portion are so pronounced that the dimensions assigned to this part determine the design of the instrument. It is debatable whether the tendency has not been to attach too much importance to this reduction in the diameter of the tube.
If an observer looks through a series of tubes of the same diam eter but of different lengths, placing his eye close to the end of the tube, his field of view will be smaller with a long tube than with a short one. The factor governing the extent of the field of vision is obviously the proximity of his eye to the front end of the tube. Thus in a periscope the only way of increasing the field of view is to locate the eye virtually near the top of the tube by inserting therein a system of lenses which, in addition to satisfy ing other conditions, will form an image of the observer's eye in the required position. These further conditions ensure the trans mission to the real eye of all the light (assuming for the moment that all losses of light on refraction through the lenses of the in strument may be neglected) that reaches the virtual eye position : roughly, they involve the insertion in the tube of a lens at inter vals proportional to the distance of the virtual eye from the open end of the tube. Thus if the field of view is to be doubled the number of lenses needed in a tube of given length and diameter must be doubled. Two tubes, the length and diameter of one being twice that of the other will give the same field of view, but the diameters of the light beams transmitted will be in the ratio two to one. Since diameter of beam and angular field are recipro cally proportional, the angular field may be doubled in the large tube for a fixed number of lenses without reducing the illumination below that obtained with the smaller tube. It follows that for a given angular field and a given diameter of emergent beam the number of lenses required is proportional to the length of the tube and inversely proportional to the square of its diameter. As an illustration, the number of lenses required to transmit a given beam down a tube three feet long and two inches in diameter will transmit the same beam down a tube 27 feet long if the diameter is increased to six inches.