Comparing aperture area of different lenses with different focal length

Started 1 month ago | Questions thread
A Marcus Junior Member • Posts: 45
Re: Comparing aperture area of different lenses with different focal length

The f-number is a value that opticians use to relate image brightness as projected by the lens. A camera lens acts like a slide or movie projector in that it projects an image of the outside world on film or digital sensor. When we take the picture we expose this image to a recording media. This is the exposure. If the amount of light is just right, the picture will be good. If the amount of light is too bright or too dim, the exposure will be wrong and the recorded picture will be substandard or spoiled.

There are zillions of different size camera lenses ranging from giant telescopes that are actually cameras to miniature spy cameras you can hide in lapel pin. In other words: a hodgepodge of lenses, all different as to working diameter (aperture) and focal length (magnifying power).

Years ago the photo industry recognized the need to find a way to standardize exposure settings. We needed a way to set a giant camera lens so that it delivered a proper picture and at the same time, a miniature camera set the same, also delivered a proper picture.

Your table of aperture areas in square millimeters is correct. You get an “A”.

I want to add a few facts that will help your understand the why?

1. The focal length determines the magnification i.e. the image size. If you double the focal length the image size changes. It becomes twice (2X) as large. Now this enlarged image will cover more space (area) on film or digital sensor. The film area or the digital sensor area is fixed so it does not enlarge, only the image is enlarged. You cannot see all of this now enlarged image because the camera uses a mask at the image plane to prevent excess image from showing. Nevertheless the image area is now twice what it was. If you enlarge a rectangle making the sides twice as large the area of the rectangle is now 4x larger. What I am saying is, double the focal length and the image area increases 4x. What happens is the image brightness drops 4x with a doubling of the image area. That is why we need the f-number. It is a ratio, independent of dimension. The f-number system takes into account the fact that the working diameter and focal length are intertwined.

2. If you double the working diameter of a lens its area changes also by 4x. This is a course adjustment. The photo industry wants a finer adjustment of just a 2x change is image brightness. We are now talking an adjustment increment that doubles or halves exposure. If you multiply or divide a circle diameter by the square root of 2 = 1.414, the revised dimeter now sports a 2x change in area. Thus the f-stop adjustment uses this increment of diameter adjustments to the working diameter of the aperture. The number sequence is: 1 – 1.4 – 2.8 – 4 – 5.6 – 8- 11 – 16 – 22 – 32 – 45 – 64 (some rounding). This is the f-number set. Each number is 1.4 times its neighbor on the left. Each number is its neighbor on the right divided by 1.4.

Keyboard shortcuts:
FForum PPrevious NNext WNext unread UUpvote SSubscribe RReply QQuote BBookmark MMy threads
Color scheme? Blue / Yellow