# What is the formula for determining where infinity focus begins?

I'm having difficulty find any info on determining where infinity focus begins. I'm assuming there's a formula involving focal length and... Can anyone help?

• Hi DavidV, Welcome to photography.stackexchange. Are you comfortable with the definition of focal-length?
– Stan
Commented Oct 23, 2017 at 2:10

The key to this answer is to first settle on the tolerable size of the circle of confusion. Most depth-of-field tables set this value at 1/1000 of the focal length. Kodak, for critical work set this value a 1/1750 of the focal length. For our purposes, we will use 1/1000. Thus if a 50mm lens is mounted the permissible size of the C of C is 0.05mm. This size will tolerate a 10X enlargement viewed from standard reading distance.

Now most depth-of-field on line calculators can be played with to discover what subject distance for a given focal length set to a given aperture will just kiss infinity. If you play with them, imputing different values, you will discover that infinity is about 4000 times the working diameter of the lens for a C of C of 0.05mm. So a 50mm lens is mounted and set to f/2. The working lens dimeter is 50 ÷ 2 = 25mm. Using 4000 times the working diameter, infinity is 4000 X 25 = 100,000mm = 100 meters = 3,937 inches = 328 feet.

The same 50mm set to f/8 has a working diameter of 50 ÷ 8 = 6.25mm. Using the 4000 rule of thumb, infinity is 25,000mm distant = 25 meters = 984 inches = 82 feet,

Let me add that I think the value of 4000 X the working diameter is too stringent. I think that 3000 X or somewhere in-between 4000 and 3000 X the working diameter is the more practical value. However, those that know me,, know I am overloaded with gobbledygook.

P.S. Infinity for an optical system is defined as that distance from the camera whereby the light rays from the subject arrive as parallel rays.

Hyper focal distance formula using 1/1000 of the focal length as C of C diameter answer in feet.

Focal length ÷ f-number X 0.033 X 1000

Lens is 100mm focal length operating at f/11

100 ÷ 11 X 0.0033 X 1000 = 30 feet

The hyperfocal distance is simply the working diameter of the lens multiplied by the agreed upon diameter of the circle of confusion. Thus if a 200mm lens is used set to f/8, the working diameter is 200 ÷ 8 = 25mm. If the circle of confusion is 1/1000 of the focal length, then 25mm X 1000 = 25,000mm, this is hyperfocal distance. 25,000mm X 0.0033 = 82 ½ feet. It’s as simple as that!

I think there's probably a misunderstanding of terminology here. Infinity focus is the situation where the lens is literally focused such that light from an object infinitely far away would convergence on the focal plane.

Only one distance can ever be in true focus at once. I think what you're looking for is something more like the hyperfocal distance — a distance where for a given aperture and recording media and definition of "acceptable focus" everything beyond that is in acceptable focus.

Or perhaps you're simply wondering what the depth of field is when focused at infinity. That depends on basically the same factors and assumptions.

I suggest you try these questions:

For practical photography (which is what we are concerned with here at Photography on Stack Exchange) it's not so much a formula as it is a definition.

Infinity for a particular lens and imaging system is the distance at which light from point sources can not be discriminated from light originating from a point source that is infinitely far away. That is, infinity for a given lens is the distance at which light from a point source appears, within the resolution limits of the imaging system, to be collimated.

Collimated light is defined as light rays from a point source that all strike the front of a lens parallel to other light rays from the same point source. When collimated light strikes a lens, the parallel rays from that collimated light will converge to a point at a distance behind the lens equal to the focal length of the lens. Light from point sources closer to the lens strike it at varying angles and will create a blur circle when the lens is focused at infinity. If the differences between the angles of light rays from a point source are small enough then the blur circle will be so small that the imaging system can not distinguish the blur circle from a singular point. If light from a point source strikes the lens at varying angles too small to be discernable from truly collimated light, then the distance of that point source of light can be said to be at infinity.

For any particular lens, the use of a smaller aperture will decrease the difference of the angles of the light rays from a point light source at a specific distance that are allowed to pass through the lens and be used in the image. This is so because the aperture limits the size of the lens' front surface that collects light that is allowed to pass through the lens. The smaller the aperture is, the lower the amount of the surface area of the front of the lens is that collects light allowed to pass through the lens. The larger the aperture is, the greater the amount of the surface area of the front of the lens is that collects light allowed to pass through the lens.

Consider a point source of light at a distance from the lens that the light striking the lens from that point source results in a blur circle just barely large enough to be seen as blur and not a point when the aperture is at a particular setting. If we stop the aperture down then the size of the blur circle is reduced. At a specific narrower aperture the blur circle will become small enough that it will appear to be no different that a discrete point of light to our imaging system.

If there is any answer to your question, we have to assume it refers to depth of field, and it would have to specifically be about hyperfocal distance.

For example, a 50 mm lens at f/4 on a full size sensor (35 mm film size sensor) has a computed hyperfocal distance of 68.5 feet (20.88 meters). Other focal lengths, apertures, or sensor sizes will have different numbers. Any depth of field calculator will show you hyperfocal. It has two meanings:

1. A lens focused at the hyperfocal distance will have just-acceptable depth of field just barely reaching to infinity (and back to half of hyperfocal).
Meaning, Depth of field calculators will then show DOF extending from half of hyperfocal to infinity.

2. A lens focused at infinity will have just-acceptable depth of field just barely reaching back to hyperfocal.

I perceive that to be what you must mean by where does infinity focus begin?
Depth of field to infinity always begins at hyperfocal.
Infinity focus is at infinity, but depth of field can have a wider span.

Very short wide angle lenses stopped well down on a fairly large sensor, and focused at hyperfocal can have extreme depth of field, from infinity back to maybe a foot or two.

However, these are maximum limits judged just barely acceptable under nominal viewing conditions. The sharpest focus will always be at the distance focused.