Why does a smaller f-number mean more light, even if the aperture diameter stays the same?
Asked 7/16/2019
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I understand that the f-number is the ratio of focal length to aperture diameter. Many explanations say that a smaller f-number means more light enters the camera. But if the aperture diameter stays constant and only the focal length gets shorter, the f-number also gets smaller. In that case, why does exposure increase if the physical opening has not changed? Is the amount of light determined only by the aperture diameter, or by the focal length-to-aperture ratio together?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
7y ago
2 Answers
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The f-number is used precisely because what counts is the f/D ratio. Assume you are shooting a grey wall. If with F=50mm you get all the photons reflected towards your front lens from a circle on the wall which is 20" in diameter, with f=100mm you will get the photons from an area which is 10" in diameter, so you get 4 times less photons. So the light you get on the sensor is proportional to the area of the lens (square of diameter) and inversely proportional to the are you see through the lens focal length (square of focal length). In other words if f²/D² is constant (which is the same as saying that f/D is constant) you get the same amount of light through.
Originally by user75947. Source · Licensed CC BY-SA 4.0
user75947
7y ago
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The key is that exposure at the sensor depends on the ratio of focal length to aperture diameter, not aperture diameter alone.
The f-number is defined as:
f-number = focal length / aperture diameter
If the aperture diameter stays the same but focal length gets shorter, the lens sees a wider angle of view. That means light from a larger portion of the scene is directed onto the sensor, so the image at the sensor becomes brighter. With a longer focal length, the lens covers a narrower field of view, spreading the scene differently and reducing the light per unit area at the sensor.
That is why two lenses set to the same f-number give the same exposure, even if their actual aperture diameters are very different. A 50mm lens at f/2 and a 100mm lens at f/2 do not have the same opening size, but they produce the same image brightness.
So: a smaller f-number means more light per unit area reaches the sensor. Aperture diameter matters, but only in relation to focal length, which is exactly what the f-number expresses.
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