rsolomon Posted February 10, 2007 Share #1 Posted February 10, 2007 Advertisement (gone after registration) i understand the role of the apeture completely - my qyestion is 1.4 / 2 / 2.8 /3.4 etc... what are these numbers a measurement of .... why are larger number smaller openings.. what does 16 represent...16 what ? i am sure there is some mathematcial / physical answer to this ... thanks Rich Quote Link to post Share on other sites More sharing options...
Advertisement Posted February 10, 2007 Posted February 10, 2007 Hi rsolomon, Take a look here i really curious on this - apeture marking question. I'm sure you'll find what you were looking for!
jameshowden Posted February 10, 2007 Share #2 Posted February 10, 2007 Hi, The numbers form a geometrical progression where each number is the preceeding number times root 2 (1.4142). It follows that the area of the openings are also a geometric progression increasing by a factor of 2 (Dimensionally Area = L squared where L is a length). So exposure is halved for one stop decreasing f number. The f numbers are obtained from the formula f = focal length/aperture (in the same units). So whatever the focal length of the lens you are using, the same f number will give you the same exposure, all other things being equal. f1 is where the diameter of the aperture - approx circular - is equal to the focal length of the lens. From the formula above, we can see that decreasing aperture diameter will give a larger f number. Hope this helps. James Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 10, 2007 Author Share #3 Posted February 10, 2007 James Thanks I have tried the formula and see how the numbers work.... I have read your post a numbers of times and I am almost to the point where I understand it. It’s actually very interesting.... do you know if this is based in some other application of science/ calculus? Is this commonly used outside of aperture definition? Quote Link to post Share on other sites More sharing options...
jameshowden Posted February 10, 2007 Share #4 Posted February 10, 2007 Hi Richard, You are right. Optics is a very interesting branch of Physics. I am not sure what you mean by "do you know if this is based in some other application of science/ calculus? Is this commonly used outside of aperture definition?" If you can clarify, I will try to answer. James R8, R6, Digilux 2, 21 - 35mm, 35 - 70mm, 60mm, 100mm, 2.8/135mm, 4/250mm Quote Link to post Share on other sites More sharing options...
stumac Posted February 10, 2007 Share #5 Posted February 10, 2007 Richard, In music, the intervals between the semitones of the even tempered scale are the twelfth root of 2. The frequency of the note is the frequency of the first note of the scale times the twelfth root of 2 times the position in the scale. Hooray for mathematics!! Regards, Stuart Quote Link to post Share on other sites More sharing options...
milsu Posted February 10, 2007 Share #6 Posted February 10, 2007 what does 16 represent...16 what ? If focal length of Your lens is 50mm, then apperture 16 means the diameter of the circle through which the light enters Your camera is 50mm/16=3.125mm. If apperture is 1.4, then the diameter is 50mm/1.4=35.714mm. Quote Link to post Share on other sites More sharing options...
jameshowden Posted February 10, 2007 Share #7 Posted February 10, 2007 Advertisement (gone after registration) Hi Stuart, That musical illustration is good. It illustrates the fact that it is mathematics which ties the universe together. And Hi Richard, I should have mentioned in my first reply that f numbers are dimensionless. They are derived from a formula where x inches is divided by y inches so the inches cancel and you are left with just a number. Of course, your units could be centimetres, kilometres or even miles. Providing both dimensions are measured in the same units, you will end up with the same dimensionless number James Quote Link to post Share on other sites More sharing options...
lars_bergquist Posted February 10, 2007 Share #8 Posted February 10, 2007 Bring out your pocket calculator and do some squares. It is roughly true that: The square of 1 = 1.4 The square of 1.4 = 2 The square of 2 = 2.8 and so forth. Equally, the root of 2.8 = 2 ... The reason why we must do doublings and halvings by squares and roots is of course that we are dealing with areas (the area of the aperture in the iris diaphragm) and not with linear measures. The old man from the Age of the Slide Rule Quote Link to post Share on other sites More sharing options...
jameshowden Posted February 10, 2007 Share #9 Posted February 10, 2007 Hi, I must beg to differ on some of your equalities. The square of 1 equals 1, not 1.4 The square of 1.4 equals 2. To an approximation, yes The square of 2 equals 4, not 2.8 The root (square root) of 2.8 equals 1.67, not 2. Check these on your calculator (or your slide rule) James Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 10, 2007 Author Share #10 Posted February 10, 2007 John's formula is right on and here what i have gotten.... sqrt of 2 = 1.414212 so as john has said 1 * 1.414212 = 1.4 1.4 * 1.414212 = 2 2 * 1.414212 = 2.8 2.8 * 1.414212 = 4 4 * 1.414212 = 5.6 5.6 * 1.414212 = 8 8 * 1.414212 = 11 11 * 1.414212 = 16 16 * 1.414212 = 22 22 * 1.414212 = 32 32 * 1.414212 = 45 45 * 1.414212 = 64 to calculate the diameter of the circle of light allowed thru equals: 50mm/16=3.125mm. 50mm/1.4=35.714mm. 100mm/16= 6.25mm 100mm/1.4=71.4285 mm so he relationship between cirle of light and focal length is clear.. what does focal length really mean ?, i have always thought is was simply the angle of view from the film plane. i see it is related to light..but how ? Since the cirle of light is twice as big on a 100 compared to a 50 mm lens ( f16 on a 100 brings in twice the circle of light as f16 on a 50) is the focal length related to the distance the light must travel ? if so there must be a "falloff" in the strength of light ? still a bit confused thanks Rich Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 10, 2007 Author Share #11 Posted February 10, 2007 i'm sorry --- James --- i called you John rich Quote Link to post Share on other sites More sharing options...
stumac Posted February 11, 2007 Share #12 Posted February 11, 2007 Hi Richard, In theoretical terms, for a simple convex lens the focal length is the distance from the center of the lens to the plane where parallel rays of light entering the lens converge to a point. Practically approximatly the distance from the lens to the image plane. I hope this makes sense to you, a good reference is the Ilford Manual of Photography, you may pick one up from a secondhand book shop, mine dates from the 1950's. Regards Stuart Quote Link to post Share on other sites More sharing options...
jameshowden Posted February 11, 2007 Share #13 Posted February 11, 2007 Hi Richard, No offence taken. John is a good name too! Stuart is right. When a lens is focussing an object at infinity, the rays of light will be parallel and the image will be at the focal point of the lens. As the object approaches the camera, so the lens has to move away from the image plane, just a bit. Because the physical size of the aperture in 100mm lens is twice as big as in a 50mm lens, but the light produces an image twice the size, there is no reduction in the brightness of the image. As you say, the focal length is related to the distance the light travels when once it has passed through the lens. You have touched on an interesting point concerning digital photography. The Digilux 2 has a longer focal length lens than a 5mp point and shoot, so the image size is larger. Therefore the individual pixels are larger and capture more light. So it produces better pictures for two reasons, 1). the superlative Leica lens, and 2). the larger pixels in its receptor. James Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 11, 2007 Author Share #14 Posted February 11, 2007 im getting closer ..... so if i understand you are saying that the amount of light coming in thru the lens and actually hitting the film is halved for a 100 vs a 50 because the image size for 100 is twice as large... this would make sense looking at the numbers below 50mm f4 area of apeture is 12.5mm 50mm f8 area of apeture is 6.25mm 100mm f4 area of apeture is 25mm 100mm f8 area of apeture is 12.5mm However, i have something wrong .... because the angle of view of a 50mm lens is 45 degrees and the angle of view for a 100mm lens is 25 degrees - doesn't this mean the image size of a 100mm is not 50% of the image size of a 50mm .... it's 55 % - and then f4 on a 50mm would a different amount of light then f4 on a 100mm lens surley i am flawed somewhere-- but i am capitvated by this Quote Link to post Share on other sites More sharing options...
milsu Posted February 11, 2007 Share #15 Posted February 11, 2007 50mm f4 area of apeture is 12.5mm50mm f8 area of apeture is 6.25mm Diameter, not area, You made a typing lapse. It is more confusing, when You know that focal lengths are not exactly what they are named, because of construction issues, for example 50mm is not really 50mm, but it differs on different lenses from around 51mm to 52mm. Maybe that is the reason why angles don't match, because 50mm lens is not actually 50mm, and 100mm lens is not actually 100mm. Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 11, 2007 Author Share #16 Posted February 11, 2007 Milos , Thanks for the guidence .. yes diameter - not area - thanks i have followed the formula and came up with : if a 50mm is really a 48mm and a 100 is really a 101mm then the same amount of light reaches the film plane with either lens at f4 or f8 ..(or any fstop) because at 48 and 101 exactly half the image is seen with the (so called) 100 mm lens thanks Quote Link to post Share on other sites More sharing options...
masjah Posted February 11, 2007 Share #17 Posted February 11, 2007 Richard For a given lens diameter, the intensity of the light hitting the film falls off as the square of the distance of the light source from the film (effectively the lens to film distance, that is, the focal length). On the other hand, for a given focal length lens, the intensity of the of the light hitting the film increases as the square of the lens diameter (because it depends on the lens area). Hence the ratio of the focal length to the diameter (which is the f number) will give you an indication of the intensity of the light hitting the film which is the same for the same f number, whatever the focal length of the lens being used. Because everything is proportional to the square of things, then doubling the f number (eg f/4 to f/8) reduces the intensity of the light by a factor of 4. Hence increasing the f number by the square root of 2 reduces the intensity of the light by a factor of 2 (one f stop). This is why single f stops are in the ratio of 1.414... (the square root of 2). Quote Link to post Share on other sites More sharing options...
jameshowden Posted February 13, 2007 Share #18 Posted February 13, 2007 Hi Richard, If you want to go deeper into photographic theory, I can recommend a book by Michael Langford called, "Langford's Basic Photography." It is not so basic as the title would have you believe. I had an earlier edition, before digital photography was even dreamed of, when I was doing an A.R.I.P. course in England. The new one is not yet released, but can be pre ordered. Chapters.ca have it listed at C$30.98. When you have digested that one, there is an Advanced Photography by the same author which is currently available from the same source at C$64.50. James Quote Link to post Share on other sites More sharing options...
rsolomon Posted February 13, 2007 Author Share #19 Posted February 13, 2007 thanks so much to all -- a good lesson... and i will look for the books !! thanks again Rich Quote Link to post Share on other sites More sharing options...
cbretteville Posted February 13, 2007 Share #20 Posted February 13, 2007 James, Thanks for the tip on Langford's new book. - Carl Quote Link to post Share on other sites More sharing options...
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