Please verify my shutter speed calculations

[paul_poropat]

<p>Hello all<br>

My digital shutter speed tester is ready to go, however I would like some of you to check the calculations that I used to convert the fractional speeds as marked on the camera to the decimal equivalent (that is the easy part). I also want to list the numbers for over and under exposure in thirds. Example: for 1/60th second equals .0166 second. Plus one third stop, .0166 x 1.3333 = .0221 second. Plus 2 thirds stop, .0166 x 1.6666 = .0276 second. Minus one third stop, .0166 x .8333 = .0133 second. Minus two thirds stop, .0166 x .6666 = .0106 second. I have a whole worksheet that I can e-mail to anyone that asks. Thanks for your assistance. Paul</p>

[bernard_lazareff]

<p>Not quite.<br>

1/3 stop = 2^(1/3) = 1.260 (not 1.333)<br>

2/3 stop = 2^(2/3) = 1.587 (not 1.666)<br>

But the difference is small as shutter accuracies go...</p>

[richard_oleson]

<p>I think my shutter speed tester has a chart like this already glued to the top of it .... if you'd like to email me for it, I'll scan it and send it to you.</p>

[charles_stobbs3]

<p>Above referenced PDF chart has at least one flaw. 1 divided by 40 does not equal .0500. Check everything.</p>

[paul_poropat]

<p>Thanks guys. I caught the mistakes on a later revision. Is there some reference I could check to learn about figuring the fractional stops for exposure? Anyway...I thought I would get straightened out on this forum. Thanks again, Paul</p>

[richard_oleson]

<p>Multiplier for 1/3 stop of shutter speed is the cube root of 2.</p>

<p>Multiplier for 1/3 stop of aperture is the 6th root of 2.</p>

[paul_poropat]

<p>So... dealing with the log nature of time like sound, I cannot just use the decimal equivalent of thirds. To gain one third more time I multiply by 1.25992105 (My instrument will display 4 decimal places), and to gain two thirds I multiply by 1.5874009. Next question is what factor to use for one half stop? and what to use for minus one third, one half, two thirds? Thanks, Paul</p>

[richard_oleson]

<p>for 1/2 stop, you multiply the square root of 2 (1.414141414). For whatever fraction of a stop you want, it's that root of two.</p>

[paul_poropat]

<p>I thought so... but I wanted that confirmed. Thanks</p>

[albert_richardson1]

<p>Do you mean that you want to set the shutter speed off by 1/3 step to get the over or underexposure you want? If so the f/stop set on the lens would be the same as for the full exposure between the various shutter speeds you use. You would time the shutter to let in the fractional amount of light between it and the next double (or half) shutter speed necessary to change the exposure. This is simply shutter speed + incremenal value of the same shutter speed. Or shutter speed - (1 - incremental value of the previous shutter speed). That is, 1/3 less light than 1/50 sec is 1/50 sec + 1/16.66 sec or 1/66.66 sec. 1/3 stop more light is 1/50 sec - 1/8.33 sec or 1/41.67 sec.</p>

<p>The difference between shutter speeds and f/numbers is that shutter speeds are a linear in nature and f/numbers are a derivitive of the intensity of the stronger light shown in a ratio comparing two light intensities. You can simply count shutter speeds and find the differences between them using a small enough common unit of measure. You only have to be aware that, as you step between half and double measures, you have to recalculate the intermediate values. This is exactly the same thing we do here in the U.S. with the breakdown of an inch on an ordinary English ruler.</p>

<p>F/numbers, on the other hand, are based on a scale built from the powers of 2. You get the same sequence of numbers whether you simply take the powers of 2 directly or whether you actually calculate the areas of the circles various apertures would occupy in an ideal lens. The f/number is always the square root of the intensity of the strongest light expressed in the form of a ratio comparing the effect of an aperture with that of the lens open to a diameter of its focal length. The aperture is always '1'. The first f/stop, for example, admits half the light of the wide open lens. The ratio 2:1 describes this relationship and can be read as 'the wide open lens admits twice the light of the first f/stop.' The f/number for this stop is the square root of the intensity of the strongest light, namely, 2. The numeric value in f/1.4 is found by taking the square root of 2.</p>

<p>The next f/stop in the sequence works the same way. This f/stop admits half the light of the previous f/stop, or only 1/4 the light the wide open lens admits. The ratio for this comparison is 4:1. Read this ratio the same way as before so that it says 'the wide open lens admits 4 times more light than the light from the second aperture.' The f/number derived from this second f/stop is f/2, where 2 is the square root of 4. The entire sequence of f/stop numbers is an extension of this same procedure.</p>

<p>The linear part of the design is in the ratios that compare the light intensities. Just as with shutter speeds I described earlier, you can find incremetal f/stop numbers by adjusting the ratio before taking its square root. 3:1 lies halfway between 2:1 and 4:1, and the f/number for it is the square root of 3 or f/1.732. 1/3 less light than f/2 is f/2.309.</p>

<p>It is not difficult to work all this out using the formula functions in a spreadsheet program.</p>

<p>I think you are confusing apples and oranges in the design of your shutter speed calculator. If you vary the exposure by changing the lens f/stop, you leave the shutter speed alone, and, if you change the exposure with the shutter speed, then the f/stop stays the same. Remember that you are not adjusting for reciprocity to get the same exposure with different settings, you are deliberately trying to get under or over exposure. You are not looking for 1/3 f/stop less light to get underexposure, you simply want 1/3 less light.</p>

[albert_richardson1]

<p>I meant to end by writing "You are not looking for 1/3 f/stop less light to get underexposure, you simply want 1/3 EV less light."</p>

<p>In short, I think you had it right the first time.</p>