International photographer (Jan-Dec 1934)

Tiventy T h INTERNATIONAL PHOTOGRAPHER December, 1934 r\rmrf~r\ LA Ik ll k \f* bears the same relation to focus in both of them, or, as \J Q I t Ix/Vll IN I INxJ generally termed, both lenses have the same relative aper 1 ■f u p fi^pp p^ tare. The ratio of 2 to 6 is as 1 to 3, or -, and the ratio I He arbbD x 3 ^^ — of 4 to 12 is as 1 to 3, or -; that is, the diameter is in OF L 3 both instances equal to one-third of the focal length of p ^J ^ C Q the lens. The aperture ratio is -. By E. W. MELSON and S. LAWRENCE The intensity ratio, as we can plainly see, is the square of Bausch & Lomb 0I the aperture ratio. We therefore conclude that: PART II ^' Speed depends on the aperture ratio, or relative aperture. In our previous comparison of the speed of two or 2. Speed is proportionate to the square of the aper more lenses we considered only the variation of one factor ture ratio. at a time, assuming the other factor, either the aperture , ™, . . . .. c i i .i , i .i • i .i n t .i o. I he same aperture ratio, or relative aperture, or the focal length, to be the same in both or all of them. , \ FCUU c> ,m A , c i i .i i-rr t »u u means the same speed. It both aperture and local length are dirrerent, the prob _ K lem of determining the relative speed becomes somewhat Thus' if we know the ratio of the diameter of aperless simple. We consider the variation in volume and ture t0 focal length, regardless of their actual measureintensity of light together— in connection with each ment.s' * IS an easv and simple matter to calculate the other — instead of separately. A certain diaphragm open relative speed. ing admits a certain volume of light. With any varia Various systems have been devised to express and tion in diameter of this opening, the volume of light mark the relative value of certain openings. Of these varies directly as the square of the diameter. The light systems we shall concern ourselves with two only, the possseses a certain intensity at the diaphragm opening. focal ratio system and the uniform system. This intensity is gradually diminished and is proportion Tl f 1 " " 11 A U " ' k A ate to the square of the distance traveled. As the relative ,. . ', ' . *-\ , ~. .. s ■ i • . i i i .i i .• • fc •«. l r l( directly on the ratio of aperture to focus. I he diameter speed ultimately depends on the relative intensity of light , , . F. . . . , . . .11.1 . i. .i v °t the aperture is represented as a fraction of the focal action on the plate, and as we cannot directly compare , . r , /0 , ,0 r , ,. , /0 . . . i j • . • ' .•«. i p. •. i . length, as f/2, f/3, f/4, f/8, etc., meaning that the volume and intensity, or quantity and quality, it becomes ,. te , , ', ' ' . ' ., ',„ ' ._ ' ,. , .„6 . , i . i u • L .-4. diameter of the aperture is 1/2, 1/3, 1/4, 1/8 and so on, necessary to have volume represented by intensity, or to , . , , , , , , , , . . t -i i .■ • «. •«. i j-nr" . r r or the rocal length of the lens, or that the aperture ratio estimate the relative intensity of different volumes of . + /0 1 , 1 ,? . , /0 ™. . F. , ..u i i.. ,i • „ a i i. ls V^> i/j> 1/4, and l/o. 1 he intensity ratio, or rela the same light at the same point. A certain volume or . .' ' .' / ' , . ' . / ' . , i i . . . • „ . x • * • -..• l • * tive intensity — relative speed — as we have previously light represents a certain amount or intensity, initial inten . . J , . K . , .. J r._ , .,/ •r ~ n •». 4. ..u • 4 u 4L 4 i „ • seen, is the square or the aperture ratio, or 1/4, 1/9, 1/16, sity we may call it, at the point where that volume is M IC\ 2, . v . . . . ' />/»/> .• . j a • i t 4.U l U4 1/ot, etc. Exposure time being in inverse proportion to estimated. An increase in volume of the same light quite i i • i i n < / / V ii j • • 4.u speed, relative exposure must be as 4, V, 16, 64, etc. naturally means a corresponding increase in the amount K ' F ' ' ' ' of intensity and vice versa. The initial intensity therefore Thus the fractional diameter gives directly, or in varies as the volume of light varies, or as the square of directly, aperture ratio, relative speed and relative ex the diameter of the aperture. As this intensity is dim posure. The ratio number 2, 3, 4, 8, etc., as denominator, inished in proportion to the square of the distance, we can with one as numerator, gives the aperture ratio; and the without further preliminaries conclude that the ratio of square of the aperture ratio gives the relative intensity or the square of aperture to square of focus denotes the relative speed — and inversely the relative exposure. The relative ultimate intensity, the relative speed. following table will help make this clear: For example let us take two lenses of respectively 2 Fraction diameter f/2 f/3 f/4 f/8 etc. and 4 inches diameter and 6 and 12 inches focus. Their Aperture ratio 1/2 1/3 1/4 1/8 etc. relative initial intensity as based on relative volume of Intensity ratio, or light is as 2 x 2 and 4 x 4, or as 4 and 16. The intensity Relative intensity 1/4 1/9 1/16 1/64 etc. is diminished in proportion to the square of the focus, or Relative exposure 4 9 16 64 etc. as 36 and 144. Therefore, the relative ultimate intensity, ^. . . , , . . ,. 1 he intensity, or speed, being in direct proportion to . the square of the aperture ratio, the speed value of any or relative speed, must be as — and — , or as and ; two openings can thus be easily compared. The speed of J" ^ f/2 and f/4 for instance, is proportionate to 1/4 and that is, the two lenses have exactly the same speed with 1/16 respectively. But these fractions compare inversely those apertures. The fraction denoting the relative ulti as their denominators, and the denominators are the mate intensity is termed the intensity ratio, or ratio of squares of the ratio numbers; consequently the speed is in intensity, and when that is the same for any two or more inverse proportion to the squares of the ratio numbers. lenses, their speed is the same. Thus the speed of f/2 compares with the speed of f/4 We can analyze this example independently of those inversely as the square of 2 compares with the square of figures. The 12 inch focus lens has twice the diameter 4, that is, inversely as 4 and 16, or directly as 16 and 4, of the 6 inch focus lens and consequently transmits four or as 4 and 1. times as much light; but the four times larger volume, Exposure time being in inverse proportion to speed after traveling twice the distance, is distributed over a (the more speed, the less exposure, and vice versa), it four times larger area, and the ultimate intensity is there follows that exposures are directly as the squares of the fore the same with both lenses. ratio numbers. Further analysis shows that the diameter of aperture It is needless to say that the same ratio number means Please mention The International Photographer when corresponding with advertisers.