International projectionist (Jan-Dec 1947)

HEKE is a simple procedure to rind the exact focal length of a projection lens or, in fact, any lens. This can be achieved without knowing anything about the lens itself — for example, the number of elements, speed, symmetric or asymmetric construction. Of course, the procedure is always useful when it comes to a lens which is unmounted or one which does not have any marking whatever engraved on the barrel. Take an opaque cardboard, preferably black, and with the point of a sharp knife make a couple of slits of about V2 inch long and x/4 inch apart as shown in Fig. la. Position behind it a frosted light blub. Not less than 3 feet away from the cardboard and facing it locate a ground glass of the type used in plate cameras. The frosted side of the glass should face the cardboard. The lens under test is first kept near the cardboard and then slowly moved away until an enlarged sharp image of the two slits is focused on the ground glass. The location of a point of the lens is recorded: for example, how far one of the rims of the barrel is from the cardboard. Now the lens is moved again toward the ground glass until a new sharp image of the slits appears focused on the ground glass. This time the image will be reduced in size. Now look at Fig. lb: again the position of the same point of the barrel is recorded. Now, collect the data. Measure in inches the fixed distance between cardboard and the ground side of the glass and designate it "D". Then measure, also in inches, how much the lens has been displaced between the two positions yielding the enlarged and the reduced image, and call the new distance "d". The formula that gives the focal length in inches of the lens is: D2 — d2 Focal length = inches. 4D This formula is read "Capital D square minus small d square, divided by four times capital D." Let us now apply the formula to the following experimental data. The distance between the cardboard and the grounded side of the glass is 40 inches. The distance we had to move a particular lens to obtain the two images as specified above was 30 inches. What is the focal length of the lens? 402 — 302 Focal length = ■ = 4 X 40 40 X 40 — 30 X 30 4X 40 1600 — 900 700 160 160 Elements of PROJECTION OPTICS By DR. ANGELOMONTANI Consulting Engineer, New York City The accuracy of the evaluation of the focal length depends on the care employed in the measurement of the distance between the cardboard and the ground face of the glass and of the linear displacement of the lens tested. Figure 2 illustrates the path that some of the most representative rays follow going from the film to the projected image. We can see at once that if we should reduce the distance between the planes Pi and P2, called the principal planes of the lens, until they coincide, the rays coming through the left side of the lens would match the rays going out through the right side. In fact, disregarding the distance between Pi and P2, we can write: Screen size Distance from Pi to screen Film size Distance from P2 to film. This is a very useful relation since it LIGHT BULB FIGURE 1 OBJECT determines what focal length lens has to be chosen to fill a screen at a predetermined distance. The lens manufacturers have already prepared tables which indicate at a glance the focal length that the projectionist must choose for every instance and therefore we are not going to apply the formula to a computation. Only purpose was to indicate how those tables are computed. The procedures given and the hint about the size of the images in relation to the focal length are based on that which is called the "focal length equation." We are not writing this equation because in its simplified form (which even today is found in college textbooks) is highly inaccurate as it does not take into consideration the lens thickness which is always a considerable amount of the focal length. The correct form is considered beyond the scope of the present exposition; also, it would be of little use to the projectionist. Composition of Lens Image Considering how a lens forms the image of an object, we may state broadly that the lens picks up point by point on one side the light received by the object and reproduces those points on the other side. Each reproduced point is in the same relative geometric sequence in the image as it was on the object, and of the same color and light value. Of course, we are now considering, for our purpose, a perfect lens. That which it is desired to stress is the fact that the reproduced or projected image is constituted of a mosaic of points of light and shade and color. Actually, the elements forming the mosaic are not points, but small discs of light, their GROUND GLASS CARDBOARD "TH'SDis^ncev "s7l5tr ATLE^FEET. GROUND SIDE "" OBJECT PREVIOUS LENS POSITION REDUCED IMAGE NEW POSITION OF THE LENS L IN ,%£_ "d" 4% inches. 18 INTERNATIONAL PROJECTIONIST March 1947