Light gain with fast lenses

Friday, September 4. 2009

Light gain with fast lenses

I was interested what difference there is between the Canon EF 50mm f/1.2, f/1.4 and the f/1.8 model regarding the light gain compared to an f/2.8 lens. The amount of light that travels through an optical system is usually given by f-numbers, the relation between focal length and aperture diameter. Doubling or halving the diameter of the aperture results in quadrupling/quartering the aperture area and thus the amount of light that can fall through:

$r^2\pi=A \,\Rightarrow\, (2r)^2\pi=4A$

Practically it is of interest what f-numbers result in doubling/halving the amount of light,

$2A=2r^2\pi=(\sqrt{2}\cdot r)^2\pi$ ,

what is thus given by an aperture diameter change factor of √2 ≈ 1.41. Continuously doubling/halving the light amount results in the diameter changing with the factors (√2)^k, yielding the classical sequence

1.4 → 2.0 → 2.8 → 4.0 → 5.6 → 8.0 → ...

The switch from a lens with maximum f/2.8 to one with f/1.4 thus yields 4× as much light, allowing ¼ of the original exposure time. Between f/2.8 and f/2.0 there’s a factor of 2. So, switching f/2.8 to f/1.8 must gain light with a factor between 2 and 4. What’s the exact amount? It’s

$\displaystyle\left(\frac{2.8}{1.8}\right)^2 \approx 2.42$

So it’s even less than 2.5, while with an f/1.4 lens it’s a factor of 4! Thus, there’s quite a difference in the light amount between those two lenses. And what about the step from f/2.8 to f/1.2? The gain factor is calculated similarly: 5.44. The step from f/1.4 to f/1.2 only yields 1.36× more light.

Posted by Stephan Paukner in Photography at 21:23 | Comments (0) | Trackbacks (0)

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