International projectionist (Jan-Dec 1957)

What Is YOUR Problem? Projection CLINIC Mirror Magnification at Constant Is the magnifying power of an arclamp mirror different in the central and edge zones? AN ARC-LAMP manufacturing firm published a table to prove that different magnifications prevail over the surface of an arc-lamp mirror; optical firms manufacturing such mirrors disagree. So the answer to the above question is negative. An arc mirror has an "elliptical" form; and one of the properties of an ellipse is that the sum of the two distances from any point on its circumference to the two foci (F1 and F2 in Fig. 1) is always constant. Conventional reflector-arc optics are based upon the ellipse and its two foci, Fx and F2. Because the sum of the lengths of the two bnes drawn from the foci to any point on the circumference is constant, the sum of the two dotted lines in the drawing is equal to the sum of the two unbroken lines. A center cross-section of an arc mirror is a portion of an ellipse having one focus at the crater of the positive carbon and the other focus at the film aperture, as shown. These correspond to the two foci of an image-forming lens. Imaging of the crater as a "spot" is nearly perfect ; and the properties of the system require definitely located foci and a constant degree of magnification by central and edge zones of the elliptical mirror. In terms of projection, the distance from the positive crater to the surface of the mirror and thence to the film aperture is always the same, no matter whether we select a point at the center of the mirror or at its edge. This means constant magnifying power and nearly perfect (anastigmatic) imaging of the positive crater upon the film aperture of the projector. Power-Finding Methods Different magnifications in different zones are a physical impossibility, forasmuch as one specific elliptical form produces two fixed foci, one focus being the place where the crater of the positive carbon is located, and the other focus being at the plane of the film aperture. The magnifiying power of a mirror may be found by two methods. We may either divide the diameter of the aperture spot by the diameter of the light source, or we may divide the working distance (mirror-aperture distance) by the "geometric focus" (mirror-crater distance). The latter method is easier to use and gives more accurate results because of the ease of measuring the working distance and geometric focus. Now, here is an interesting fact. It will be found, by measuring the magnifications of a large number of arc mirrors, that the magnifying powers of most modern American mirrors intended for use with 9-, 10-, and 11-mm carbons ranges from 5 to 6, while most German mirrors intended for use with the same size carbons have magnifications of from 6 to 7. Lower magnifications are found only in mirrors such as the Weule 540/180 intended for use with 13.6 or 14-mm positives. This special German mirror has a magnification of only 4.5 and a diameter of 21.26 inches, making it larger than any American mirror. The reason for the higher magnifications of German mirrors is simply the use of correct optical principles, thus assuring more uniform screen illumination— about 75% side-to-center as com Mirror FIG. 1. A cross-section of the lamphouse as an ellipse. pared with only 55% in the case of the newer American mirrors for 9-, 10-, and 11-mm positives. Magnification Under 5? How great should the magnifying power of an arc mirror be? THE GREATER the magnifying power of an arc-lamp mirror, the less deep its curvature, and the less strongly it bends the light rays it receives from the luminous positive crater. And because an elliptical arc mirror functions like an anastigmatic optical system, its focal properties and magnifying power cannot be changed (unless auxiliary lenses are used) without disturbing its anastigmatic characteristics. As Fig. 2 shows, too small a working distance for a given mirror creates a .condition of "over-parabohzation" while also decreasing the magnifying power, and too great a working distance creates spherical aberration while simultaneously increasing magnification. There is, however, a slight leeway in working distance permitted by most manufacturers, a longer-than-normal working distance giving a more uniformly lighted screen, but occasioning a small loss of total light. Working Distance A properly positioned arc mirror will have one of its two foci at the positive crater and the other at the film aperture, as the top diagram shows. Shortening the "working distance," as in the middle diagram, necessitates moving the crater farther from the mirror, and produces a smaller aperture spot. The lower diagram illustrates the reverse effect of lengthening the working distance: the crater must be moved closer to the mirror, giving a larger spot. Working distance may be varied within a range of from 2 to 4 inches (depending upon the characteristics of the mirror) to give the precise amount of crater magnification desired; but beyond these limits, the elliptical curvature of the mirror will no longer be correct, and light will be wasted. Too short a working distance (middle diagram in Fig. 2) has the effect of increasing the "eccentricity" of mirror curvature in excess of the required degree. In addition to being too small, therefore, the spot may become brighter at its edge than at its center and have the appearance of a ring of light. Too long a working distance (lower diagram in Fig. 2) has the opposite effect, decreasing mirror eccentricity below the amount required. This produces spherical aberration, a serious defect; and the resulting spot, in addition to being large, is diffuse with an extended 20 INTERNATIONAL PROJECTIONIST • JUNE 1957