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Thread: Physics/math question

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    Senior Member apicius9's Avatar
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    Physics/math question

    Sorry for the stupid question, I'm a bit physics-challenged:

    If I use a 50mm lens at a distance of 10', will I get the same frame of the object with a 60mm lens at 12' - or is there anything else to consider? This is just about the distance, of course there may be other differences with OOF area etc.

    Thanks,

    Stefan

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    Senior Member pellicle's Avatar
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    Re: Physics/math question

    it will be close, but its a complex question and to answer correctly needs quite some calculations. However the normal angle of view of the lens is related to infinity, recall that as you focus closer you essentially extend the lens (note how a lens gets longer as you focus to 1 meter). Focusing a 50mm or a 60mm to 25.4cm and 30.4cm respectively (god I hate mixing metric with that archaic stupid imperial system so I have converted your arbitrary numbers of 12 inches and 10 inches to a similar system to which we are measuring focal length in)

    so I don't think that's a factor because we are "extending" the lens so much as to make the angle of view less significant here (much will fall off the sensor as the cone extends with the lens moving away from the sensor).

    I think that the "magnification" will be the easiest to work with here.... so:

    When focused at 25.4cm the 50mm will be extended to about 62mm from the sensor (mag of 0.24) and the 60mm (focusing on 30.4cm) to about 75mm (mag of 0.25).

    meaning it's gonna be real close

    ok ... so why do you ask "grasshopper"?

    (pardon the kung-fu reference)

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    Senior Member apicius9's Avatar
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    Re: Physics/math question

    Thanks pellicle. It's really just a very simple reason: I have some nice 50mm manual lenses but find myself still eying 57 or 58mm lenses - I'm just trying to do a reality check and convince myself that I won't lose much by going one or two steps closer and it will be much cheaper than buying a longer lens Of course, I know that there is more than just object size to that. How do others see that - is there an added benefit in a 58mm lens over a 50mm that justifies the expense to own both? I am mostly thinking about portraits here. Oh, and I grew up in Europe, so I can think much better in metric

    Stefan

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    Senior Member pellicle's Avatar
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    Re: Physics/math question

    Stefan

    I've tried to compare 45 and 50 as well as 18 and 28 and what I see (when photographing something at less than 5 meters) are subtle background changes and surprisingly similar DoF.

    for example, this is 20mm vs 28mm



    some more samples (and better res) on my blog "discussion with myself" on that choice here.

    I agree about what you say, and would not bother with such a close focal length set (I debate the 20mm vs the 28mm based on cost and AF features; meaning I can reliably give the camera to someone else to use)

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    Subscriber Member Jonathon Delacour's Avatar
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    Re: Physics/math question

    Quote Originally Posted by apicius9 View Post
    Sorry for the stupid question, I'm a bit physics-challenged:

    If I use a 50mm lens at a distance of 10', will I get the same frame of the object with a 60mm lens at 12' - or is there anything else to consider? This is just about the distance, of course there may be other differences with OOF area etc.

    Thanks,

    Stefan
    I love this kind of question because I like to know for any given focal length at a few different distances what the horizontal and vertical fields of view are likely to be. I'm not the slightest bit interested in diagonal fields of view because we see the frame in terms of what it takes in horizontally and vertically.

    So that, if I'm shooting with (say) a 20mm lens on an m4/3 camera and my "subject" is 9 feet away, I know that the area framed will be about 8 feet by 6 feet. Whereas if I'm shooting at the same distance with a 40mm lens on a full-frame DSLR, the frame will measure about 8 feet by 5.5 feet.

    There are various online field of view calculators but, for your question, the Bob Atkins calculator is most useful.

    50mm lens at a distance of 10':



    60mm lens at a distance of 12':



    So you can see that, as you suspected, the 50mm at 10ft yields the same field of view as the 60mm at 12ft. Although, because the Bob Atkins calculator assumes a 3:2 aspect ratio, on an m4/3 camera the vertical field of view has to be multiplied by 1.125)

    Quote Originally Posted by pellicle View Post
    (god I hate mixing metric with that archaic stupid imperial system so I have converted your arbitrary numbers of 12 inches and 10 inches to a similar system to which we are measuring focal length in)
    I'm happy to mix metric and imperial units but have also assumed that Stefan was thinking in feet because he wrote 10' (rather than 10"). Although it doesn't really matter because the Bob Atkins calculator is unit-independent.

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    Senior Member pellicle's Avatar
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    Re: Physics/math question

    Jonathon

    Quote Originally Posted by Jonathon Delacour View Post
    There are various online field of view calculators but, for your question, the Bob Atkins calculator is most useful.
    I used the one in my palm pilot ... mainly because I've had it for a decade and know it well ;-)
    So you can see that, as you suspected, the 50mm at 10ft yields the same field of view as the 60mm at 12ft. Although, because the Bob Atkins
    ...
    I'm happy to mix metric and imperial units but have also assumed that Stefan was thinking in feet because he wrote 10' (rather than 10"). Although it doesn't really matter because the Bob Atkins calculator is unit-independent.
    feet! ... right ... should have thought it wasn't macro ... still only the numbers would change at a constant ... (that being 12) thanks for double chekkin my math ... I was a bit worried about decimal rounding as I didn't use all the decimal places ;-)

    PS: as your an Ozzie I'm guessin that you went to school pre-decimal conversion (was that 1968?) either that or you've worked in the trades cos they're still mired with that system :-)

    thank god science uses metric and SI

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    Subscriber Member Jonathon Delacour's Avatar
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    Re: Physics/math question

    Quote Originally Posted by pellicle View Post
    PS: as your an Ozzie I'm guessin that you went to school pre-decimal conversion (was that 1968?) either that or you've worked in the trades cos they're still mired with that system :-)
    Yep, I was finishing school during the decimal conversion and working part-time at Woolworths! But I studied science at university so I can flip back and forth between metric and imperial without any problems. Feet/inches/meters/millimeters/kilograms/grams/pounds/ounces/pints/liters -- they're all the same to me. Although I think the world would be a better, happier place if everyone used metric measurements. (He would say that, you might be thinking, with his French ancestors.)

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    Administrator Bob's Avatar
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    Re: Physics/math question

    metric vs Imperial is not quite so clear since in the U.S. our gallons are smaller. Several common grocery items have begun to mark their contents in metric; the new jars being priced the same, but interestingly now contain less. I suppose that it won't be long before the government finds out that it might keep the price of gasoline the same on a per-gallon basis by raising the taxes and shrinking the gallon LOL
    Seriously, I flip bank and forth fairly easily, but here, strangely enough, we refer to pounds and oz and "English" measurements, which they are not.
    These issues are nothing compared to all the ways in common use one might use to express a location. degrees, minutes, seconds, decimal degrees, degrees and decimal seconds, and there are other systems as well not to mention the selection of possibilities in map datum.
    -bob

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    Subscriber Member Jonathon Delacour's Avatar
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    Re: Physics/math question

    Quote Originally Posted by Bob View Post
    metric vs Imperial is not quite so clear since in the U.S. our gallons are smaller.
    Bob, that's something that -- after diluting vast quantities of HC-110 over a period of nearly twenty years -- I should certainly have remembered: an Imperial gallon is 4.546 liters whereas a US gallon is 3.785 liters.

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    Senior Member pellicle's Avatar
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    Re: Physics/math question

    Quote Originally Posted by Jonathon Delacour View Post
    HC-110 over a period of nearly twenty years -- I should certainly have remembered: an Imperial gallon is 4.546 liters whereas a US gallon is 3.785 liters.
    been using 3.8 myself ... too slack to measure that carefully

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    Re: Physics/math question

    between a 50mm and a 58mm, there is more compression of features in portraits. the longer lenses flatten features more.
    you could probably see the difference better between 85mm versus 105mm for example, but at 50 or 57 it is just too close.
    however, if you take indoor and environmental portraits, i would think a shorter portrait lens allow you to work closer to the subject, and on m43, i would prefer a 35mm or 40mmm.

  12. #12
    Abbazz
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    Re: Physics/math question

    Quote Originally Posted by apicius9 View Post
    Sorry for the stupid question, I'm a bit physics-challenged:

    If I use a 50mm lens at a distance of 10', will I get the same frame of the object with a 60mm lens at 12' - or is there anything else to consider? This is just about the distance, of course there may be other differences with OOF area etc.
    Not such a stupid question seeing the amount of debate it generates...

    To answer simply: you can not get the same view at 10' and at 12', because the perspective varies with the distance to the subject. To get exactly the same view, you would have to take both pictures at the same distance from the subject and then to crop and enlarge slightly the one taken with the shortest focal length.

    From the same distance, you always get the same perspective, whatever focal length you use. It you take a photograph with a 100mm lens and then another with a 20mm lens from the same spot, you could always crop the one taken with the 20mm lens to make it look exactly like the one taken with the 100mm. If you don't believe me, try it by yourself!

    Cheers!

    Abbazz

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