Lens diameter question

[Jason Kinsey]

I was talking with a friend the other day and we started discussing lens diameter with respect to exposure, etc. Say you have a 200mm f/4 and a 200mm f/2.8 lens. Same subject, lighting, etc AND they are both shot at the same aperture (say f/5.6). The aperture is the same, but the objective diameter of the lens is larger. Wouldn't this change your exposure on a subject? It seems like you are letting in more light to begin with, so a faster shutter speed would give you the same exposure? Or maybe I am way off the mark here??

The particular interest of this discussion was supertelephoto lenses-say a 400mm f/2.8 with 1.4x converter vs. a 500mm f/4 for low light work. It seems that the 400 wins out with its larger diameter (weight, focal length, etc. are irrelevant here, just theoretically speaking). Thoughts???

[Roger Clark]

Jason,

Regardless of maximum aperture, if both your 200 mm lenses are set to f/5.6, the effective aperture is now 200/5.6 = 35.7 mm diameter. Since both lenses have the same focal length, the exposure is the same.

The effective lens diameter collects the light, the focal length spreads out the light and the pixels collect the light.

A 400 f/2.8 +1.4x TC = 560 mm f/4 versus a 500 mm f/4 are not exactly comparable. The 400 mm lens has a diameter of 400/2.8 = 142.9 mm while the 500 f/4 has a diameter of 125 mm. So the 500 collects total less light, and the 400 collects more light but the longer focal length with the TC spreads it out more. So while the exposure per pixel (assuming we are using the same camera on both lenses) is the same, the 400 mm system has 12% more detail (linear measurement). Most would judge the 400 better assuming equal optical quality due to slightly more resolution and pixels on subject with the same noise per pixel.

More/related information on my site:

Night and Low Light Photography with Digital Cameras:
http://www.clarkvision.com/articles/...ht.photography

and:

Telephoto Reach and Digital Cameras
http://www.clarkvision.com/articles/telephoto_reach

Roger

[Jason Kinsey]

Thanks for the reply, Roger. The focal length divided by the aperture being equal was the other side of the discussion, and it appears that is the correct answer. Would having more light entering into a larger diameter lens then lead to a brighter viewfinder?

[Roger Clark]

Thanks for the reply, Roger. The focal length divided by the aperture being equal was the other side of the discussion, and it appears that is the correct answer. Would having more light entering into a larger diameter lens then lead to a brighter viewfinder?

Hi Jason,
Not really because both lenses were the same f-ratio. But having said that, there is an often overlooked caveat to the same f/ratios delivering the same light. That is true for extended sources, but not point sources like stars (or catchlights from a distant animal). When the light is a point source, effectively smaller than a pixel, then the larger diameter lens will show fainter point sources and the points will appear brighter. So in the 400 versus 500 mm case, the 400 mm lens will record fainter stars in the same exposure time and all the stars will be slightly brighter. Aperture diameter wins in that case.

Roger