Motion Picture News (Oct-Dec 1927)

1916 Motion Picture News Projection Optics, Electricity, Practical Ideas & Advice Inquiries and Comments The Computation of Spotlight Diameters N view of the fact that spotlights are in such common use in theatres, it is remarkable that so little has been published concerning the optical workings of these light projectors. This lack of printed information, naturally, has resulted in the average projectionists remaining in ignorance of the fundamentals governing spotlight operation, from an optical standpoint. Mechanically, the spotlight is a comparatively simple affair, and there are few experienced projectionists who cannot walk into the projection room of any theatre and give satisfactory spotlight performance Optically, however, the spotlight is but little known, and there are, indeed, few projectionists who can, with any given set of conditions, calculate in advance what size of "spotlight" or "flood" will be obtained when the lamp is trained onto the stage. "What Causes Ghost?" Ever the presence of the central "ghost" in the light beam is a mystery to the average projectionist, and it seems impossible to make him understand that this "ghost" is the result of using uncorrected condenser lenses, and is caused by spherical aberration in the lenses, bending the edge light rays down toward the center of the beam. This, in turn, causes the "spot" to have bright edges and makes the center of the "spot" appear darker by comparison. When the spot is focussed to its smallest size the ghost formed by errors in the lens is not visible, but another ghost may appear if the center of the positive carbon has a deep depression since, under this condition, the crater is practically being imaged to form the small spot and the dark center of the crater shows up in the spot on the stage. Most projectionists believe that the ghost which appears when the spot is spread out into a flood is also a result of the condition of the crater, but this is not true, since spherical aberration in the condenser lens is responsible for it. Hoiv to Calculate "Spot" Size The writer does not recall ever having seen in print a method for calculating the size of the spot which would be obtained for a given set of conditions and for any degree of focussing. Recently, however, he received a report from F. A. Benford, of the General Electric Company at Schenec tady, N. Y., which was prepared at the request of some one who wished specific information on a method for making such calculations. We are printing much of Mr. Benford 's report, and are giving his formulas in the hope that they may be of service to those projectionists who wish to keep them on hand for reference purposes. Benford 's report is as follows : "To the best of the writer's knowledge there has never been given, in the optical treatises that are ordinarily available, a rule for finding the size of spot given by a condensing lens when used as a "spotlight." The reason for this omission is, obviously, the fact that the position of the light source in spotlight practice is between the principal focal point and the condenser; that is, the operating focal length, F, is less than the principal focal length, Fo, of the lens, and the ordinary rule relating object, image and focal length does not apply. "A further reason is the fact that an image is not formed, and the beam must be investigated through some other property than that of imagery. "It is self-evident that the accuracy of conditions are not severe in a problem of this nature, and, therefore, simple methods are to he preferred. In the following solution the accuracy is about as good as the fundamental data of a condensing lens. Thus a condenser rated at 9 inches focal length will vary nearly 0.40 inch between the focal length of the center and the focal length of the edge; and, moreover, the focal length is different, depending upon the direction of passage of light, whether from plane to convex, or from convex to plane. Some experimental data bearing on this phase will be given later. Hoiv Formula is Derived "Suppose a light ray is traced from the principal focus to the condenser (at a distance Fo from the focal plane) to the edge of the lens and this ray makes an angle with the axis that is evaluated from the equation : width of the beam is obviously W b a s Ta ngent D 2Fo where d is the active diameter of the lens. a "We may regard this angle — — as a 2 constant for any given lens, and this assumption is the basis of the following solution : From any point on the axis, a ray to the same point on the lens will suffer an a equal refraction, , and given an initial 2 b angle , with the axis, the angular half 2 where ■ ■ is the angular radius of the 2 light source as measured from the edge of the lens. b "The angle is obtained from the 2 b d relation tangent and 2 2F Tangent r cos. 2 F When F is less than Fo, the angle W will be positive, indicating a diverging beam, but when F is greater than Fo, the beam will converge to a focus (image) and then, space permitting, it will diverge into a "spot." "The initial diameter of the spot can be computed from the relation 2 r T D = ■ One Fo where D = diameter of spot, in inches, r = radius of light source, in inches. T = throw, from lens to screen, in inches. •Fo = focal length of condenser, in inches. "The initial size is the least size to which it is possible to reduce the spot by sharp focussing. Correction for Distortion "If an arc or a monoplane filament is used as the light source, the computation of is influenced by the fact of the source being foreshortened when viewed at a large angle from the normal. In this case 2b r cos. Tangent " It is customary to place the light source between the condenser and the focal point, rather than beyond the focal point, because the first position gives much higher intensities in the spot. "It is an experimental fact of common observation that the outer part of a 'spot' (Continued on page 1918)