Why do lenses with the same f-number give the same exposure despite different sizes?
Asked 4/11/2015
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If a longer lens at the same f-number has a larger entrance pupil, it seems like it should collect more light than a shorter lens. For an object at infinity, I was thinking all rays from one on-axis object point would be focused onto one sensor pixel, so the light on that pixel should depend only on pupil area, not focal length.
What optical effect am I missing? Ignoring transmission losses and T-stops, why does the same f-number correspond to the same image brightness/exposure across lenses of different focal lengths?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
11y ago
2 Answers
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The light IS (inversely) proportional to the focal length. A long telescope at high magnification sees a dim image. Binoculars are short, and see a brighter smaller image.
Yes, a 200 mm f/4 lens is 2 times the diameter, and 4x the area, which passes 4 times the light, compared to a 100mm f/4 lens. However, focal length also involves magnification, and the 200 mm lens projects the object image at 2x distance, which is 2x larger, so the image of the object is now 4 times the area (of the 100 mm lens).
4x light in 4x area is the SAME light per unit area, i.e., the SAME light intensity... the same exposure.
This is WHY the f/stop method is invented and used, so that f/4 is f/4 in any lens... so we know what f/4 means for any lens.
Sure, lens efficiency can vary slightly with number of glass elements and coatings (T-stops), but the general principle is f/4 is f/4, regardless of lens details.
Originally by user38978. Source · Licensed CC BY-SA 4.0
user38978
11y ago
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The missing piece is image size.
A longer lens at the same f-number does have a larger aperture diameter, so it collects more total light. But it also produces a larger image of the subject because magnification increases with focal length.
Example: a 200mm f/4 lens has a pupil twice the diameter of a 100mm f/4 lens, so its aperture area is 4× larger and it gathers 4× as much light. However, the image formed by the 200mm lens is also 2× larger in linear size, which means 4× larger in area.
So the 4× extra light is spread over 4× more image area. The result is the same light per unit area on the sensor: the same image irradiance, which is what exposure depends on.
That is why f-number works across focal lengths: it expresses aperture size relative to focal length, and that ratio determines image brightness at the sensor (ignoring transmission losses, where T-stops matter).
For a single ideal point, many rays do meet at one image point, but for a real image the longer lens enlarges the whole projected scene, so brightness per sensor area stays the same at the same f-number.
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