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Thread: How focal length affects aperture?

  1. #1

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    How focal length affects aperture?

    Dear all,

    Can't figure that. I know the formula is f = Focal Length / Entrance pupil, but, it is not at all intuitive for me that if you have light from a point at infinity falling on two lenses A and B, both with the same entrance pupil, both converging that light to points: fa at 150mm from the lens and and fb at 300 mm from the lens, for me, it is the same amount of light on both images. How come that lens A is one f stop brighter and will need half of the exposure time compared to B?

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  2. #2

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    Re: How focal length affects aperture?

    Because, in your diagram, can you see that the camera body for the 300 mm lens will need to be, physically, twice as long to bring the image into focus at the film plane.

    So, the same amount of light will need to travel twice as far.

    In my practice of building simple lens sliding box cameras I've come to see focal length as not just the determinant of angle of view but also the determinant of how far the light needs to travel within the camera body to arrive in focus at the film plane.

  3. #3

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    Re: How focal length affects aperture?

    Thank Ray for this insight. I understand that light becomes weaker with distance when it is diverging, when it is spreading onto surfaces that are bigger with the square of the distance. But in the case of lenses light is converging and should not, for this reason, should not lose strength for travelling longer distance. I assume it does, I just don't understand how.

  4. #4

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    Re: How focal length affects aperture?

    Quote Originally Posted by lungovw View Post
    Dear all,

    Can't figure that. I know the formula is f = Focal Length / Entrance pupil, but, it is not at all intuitive for me that if you have light from a point at infinity falling on two lenses A and B, both with the same entrance pupil, both converging that light to points: fa at 150mm from the lens and and fb at 300 mm from the lens, for me, it is the same amount of light on both images. How come that lens A is one f stop brighter and will need half of the exposure time compared to B?

    Click image for larger version. 

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    If you have a pinpoint light source at infinity (such as star light) in such a case it is the actual physical size of the aperture (same in your case?) and not the f number that determines the exposure. A fact well known to astro-photographers. For a pinpoint light source at infinity if the physical aperture size is the same in your lenses the exposure is the same too.

  5. #5
    ic-racer's Avatar
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    Re: How focal length affects aperture?

    The angle of view in A is greater (you don't show this so the diagram is not correct) and it collects more light to a smaller area making the image brighter.

    To clarify your original post title, focal length has no effect on aperture size, they are independent. Focal length affects F-number.

  6. #6
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    Re: How focal length affects aperture?

    Quote Originally Posted by lungovw View Post
    Dear all,

    Can't figure that. I know the formula is f = Focal Length / Entrance pupil, but, it is not at all intuitive for me that if you have light from a point at infinity falling on two lenses A and B, both with the same entrance pupil, both converging that light to points: fa at 150mm from the lens and and fb at 300 mm from the lens, for me, it is the same amount of light on both images. How come that lens A is one f stop brighter and will need half of the exposure time compared to B?

    Click image for larger version. 

Name:	focal-length-aperture.jpg 
Views:	29 
Size:	11.0 KB 
ID:	152827
    Your illustration shows what appear to be collimated light passing through a lens and converging to a point, which seems unrealistic to me. You have point objects in the distance that are rendered as point objects on the film plane, and areas of light in the distance that are rendered as areas of light on the film plane. The usual diagram showing resolution of distant point objects shows divergence from the object to the aperture, and convergence behind it, but even that is useful more for showing how a lens resolves than how it captures light.

    Consider this: The exit pupil is what the film sees. That exit pupil is controlled by the aperture, and is always smaller than the film. Thus, the light is spreading from the exit pupil to the film, and is thus subject to the inverse square law. The better illustration is therefore rays converging at the lens, crossing at the rear nodal point, and then diverging to the film, the opposite of your diagram.

    Rick "all models are false, though some are useful" Denney

  7. #7

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    Re: How focal length affects aperture?

    Great, thanks Pfsor, considering what you said I started to figure it out. If instead of pinpoints we imagine minimal surfaces, it is a fact that shorter focal lengths will project smaller images than the longer ones. So the same amount of light, captured by the same entrance pupil, will concentrate in smaller surfaces on film and in this way will be actually brighter. Could we say that? Any thoughts?

  8. #8

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    Re: How focal length affects aperture?

    Do not think of it as light growing 'tired' because it has to travel a longer distance. Think of it as that a bunch of light rays from an object falling all over the surface of the lens. They get bent to converge towards the focal point on the film plane. So what the film plane sees is a bunch of rays emanating from the aperture of the lens. Now if the same aperture is further away, it is going to look smaller and consequently dimmer. Think of looking at the disc of a torchlight from 1 ft away vs 10 ft away. It is the light collecting ability that is affected by the apparent diminishing of the size. That is why the moon which reflects a pale light from the sun (but is closer to us) looks brighter than a star which is boiling cauldron of energy which is much further away.

    Cheers, DJ

  9. #9

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    Re: How focal length affects aperture?

    Ic-Racer, the diagram does not consider an angle of view, just one point shedding light onto the lens. Exactly as Pfsor put it, like a pinpoint star. I think, if I understood you correctly, that is not right to say that a wide angle lens collects more light than a telephoto lens. For a wide angle using a very small film size works as a telephoto lens. Agree that it would be better to put is as "How Focal length affects F-number".

  10. #10
    Jac@stafford.net's Avatar
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    Re: How focal length affects aperture?

    Quote Originally Posted by lungovw View Post
    For a wide angle using a very small film size works as a telephoto lens.
    Technically, it is a long lens. Telephoto lenses are shorter physically than their effective focal length.

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