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Old June 11th, 2010, 01:38 PM
Doug Kerr Doug Kerr is offline
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Join Date: May 2006
Location: Alamogordo, New Mexico, USA
Posts: 8,634
Default The "light gathering power" of a lens

We don't often encounter here the phrase "light gathering power of a lens", since most technical discussions here are relatively "scientific". Still, it can be an attractive phrase when we are trying to explain the significance of the f-number to a newcomer. But like much "folk wisdom", we have to be careful not to take it at face value, or we can lead ourselves into some misunderstandings.

Let me give a little review of the situation.

Imagine we have a certain interchangeable-lens camera, at a certain location, aimed at a certain scene. We have two lenses we may wish to consider, a 50mm f/2.0 lens and a 100mm f/2.0 lens. We will use both at their maximum apertures.

We will consider a certain small area on on the subject, perhaps a skin region with an area of one square centimeter.

It turns out that the 100mm f/2.0 lens gathers four times as much light from that skin region as the 50mm f/2.0 lens. Why? Because the area of the entrance pupil (the hole though which the lens gathers light) in the 100mm lens is four times as big. (The diameter of the entrance pupil of the 50mm f/2.0 lens is 25mm; for the 100mm f/2.0 lens, it is 50mm.)

Then why do we get the same photometric exposure - and thus the same exposure result - in the two cases?

Because in the case of the 100mm lens, the image of that skin region on the sensor or film is twice the linear dimensions (and thus four times the area) of the image of that skin region when using the 50mm lens. (That might be why we would prefer to use the 100mm lens!) The light gathered from that skin region are now is spread over four times the area. If we want the same photometric exposure (which is luminous flux-time per unit area), we had better gather four times as much light. And we do - so everything is copacetic.

But, back to the phrase, we need to remember that, quantitatively, the f-number of two lenses only tells us their relative "light gathering power" if a consistent focal length is involved.

Best regards,

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