Topics Covered:

  • Typical F-numbers for various scenarios
  • How to find f-stop
  • T-stop
  • The F-numbers of the Eye

If I could steal someone’s dream myself, I’d have to go for one of Orson Welles – Christopher Nolan

We have all the formulas we need to calculate f-numbers at various ISOs based on lux levels. Here is a table that assumes a 1/50s shutter speed (which is typically used for 24fps) (Click to enlarge):


What do we learn from the above table?

Traditional films were rated at about 100 ASA (ISO). If you look at the f-numbers under ISO 100, you’ll realize why many manufacturers have f/2.8 lenses in their lineup – especially the zooms. At ISO 100, a typical zoom can shoot in a studio lit by standard lamps.

f/2.8 can also be used outdoors on overcast days. In a stadium, an f/2.8 zoom can cover any scenario during the day. During night events, the stadium is lit to about 1000 lux, and f/2.8 can still be used.

In today’s world, film is usually rated at ISO 800 on average, and you’ll find that f/2.8 can be used in a typical living room. This also makes it a great documentary or wedding f-stop to use.

Lenses with f/1.4 to f/1 can be used in low-light situations with ISO 100. On the other hand, on a bright sunny day, you will need an ND filter to even begin shooting, as the smallest f-number on typical 35mm cameras is about f/22. You might just be able to get away with f/16 on ISO 50.

What about a moonless night? Forget it. Such a camera and lens combination doesn’t exist. On a full moon night, you might just get away with an f/0.7 lens at ISO 20,000 – but you can’t buy such a lens!

On Barry Lyndon, Stanley Kubrick used a special f/0.7 Zeiss lens on ISO 100 stock pushed to ISO 200. What was his lux level? About 10 lux or one footcandle. That’s the power of three candles!

How is the f-number derived?

The f-number is derived from the following formula:

f-number = Focal length in mm / Diameter of the aperture in mm

If I have a 50 mm lens that has a maximum f-number of f/1.4, the size of the opening is 35.7 mm. At f/8, the opening is 6.25 mm. Making lenses with larger than f/1 apertures is tough – not only will the length of the lens increase (due to increase in focal length), but its width as well. Such lenses are specially designed for photography in space.

T-stop

Light enters a lens and leaves it. Is 100% of the light passed without loss? Never. The formula for f-number does not take into account this loss.

In photography, this is fine, as each exposure produces only one image. Slight errors in exposure can be corrected in post production without a large penalty in time and money. And smaller f-numbers look pretty on the advertising brochure.

In cinematography or videography, however, the camera might be moved from areas varying in brightness. It is critical that the DP know exactly how much light is passed through his/her lens. Correcting these errors is time-consuming and expensive.

For this purpose, cinema lenses usually are rated with the T-stop, instead of the f-stop. T stands for Transmission. Each lens is factory calibrated and rated in T-stops. This number is usually higher than the f-number of the lens.

E.g., if a lens has a theoretical f-number of f/1.4, and it eats 25% of light passing through it, the T-stop is approximately T/1.7.

The general rule of thumb is: If you have a lens rated in T-stops, use that number for further calculations. And try not to mix and match lenses with and without T-stop ratings on the same shot!

Finally, we have enough information to calculate:

The F-stops of the eye

According to eye geometry, if the focal length is 16.67mm to 22.22 mm, and the maximum pupil size is about 9 mm, the largest f-number of the eye is f/1.8 to f/2.5. When narrow, the pupil diameter is about 3 mm, and the f-number closes down to f/5.6 to f/7.4. On average, the pupil stays at about 4 mm, with an f-number of f/4 to f/5.6.

On average, one can say that the f-number of the eye varies from about f/2 (when it’s dark) to about f/8 (when it’s very bright) (Hecht, Eugene (1987) Optics (2nd ed.).

It is important to note that these are simplistic calculations. Precise calculations will need to take into account the specific geometry of the eye, the refracting properties of the liquids within the eye, accommodation, etc.

Takeaways:

  • F-numbers are theoretical values.
  • T-stop or transmission stop is more accurate than the f-number because it takes into account the light lost within the lens during transmission.
  • The f-number or f-stop of the eye varies between f/2 and f/8.

Links for further study:

Next: Sensitivity and ISO of the Human Eye
Previous: How to Read Light for Exposure