What is the focal length of the human eye?

It’s funny the associations people make between cameras and the human eye. Megapixels is one, but focal length is another. It probably stems from the notion that a full-frame 50mm focal length is as close as a camera gets to human vision (well not quite). While resolution has to do with the “the number of pixels”, and “the acuity of those pixels”, i.e. how the retina works, the focal length has to do with other components of the eye. Now search the web and you will find a whole bunch of different numbers when it comes to the focal length of the eye, in fact there are a number of definitions based on the optical system.

Now the anatomy of the eye has a role to play in defining the focal length. A camera lens is composed of a series of lens elements separated by air. The eye, conversely, is composed of two lenses separated by fluids. In the front of the eye is a tough, transparent layer called the cornea, which can be considered a fixed lens. Behind the cornea is a fluid known as the aqueous humor, filling the space between the cornea and lens. The lens is transparent, like the cornea, but it can be reshaped to allow focusing of objects are differing distances (the process of changing the shape of the lens is called accommodation,and is mediated by the ciliary muscles). From the lens, light travels through another larger layer of fluid known as the vitreous humor on its way to the retina.

When the ciliary muscles are relaxed, the focal length of the lens is at its maximum, and objects at a distance are in focus. When the ciliary muscles contract, the lens assumes a more convex shape, and the focal length of the lens is shortened to bring closer objects into focus. These two limits are called the far-point and near-point respectively. 

Given this, there seem to be two ways people measure the focal length: (i) diopter, or (ii) optics based.

Focal length based on diopter

To understand diopter-based focal length of the eye, we have to understand Diopter, or the strength (refractive power) of a lens. It is calculated as the reciprocal of the focal length in metres. The refractive power of a lens is the ability of a material to bend light. A 1-diopter lens will bring a parallel beam to a focus at 1 metre. So the calculation is:

Diopter = 1 / (focal length in metres)

The average human eye functions in such a way that for a parallel beam of light coming from a distant object to be brought into focus, on the retina, the eye must have an optical power of about 59-60 diopters. In the compound lens of the human eye, about 40 diopters comes from the front surface of the cornea, the rest from the variable focus (crystalline) lens. Using this information we can calculate the focal length of human eye, as 1/Diopter, which means 1/59=16.9 and 1/60 = 16.66, or roughly 17mm.

Focal length based OPTICS

From the viewpoint of physical eye there are a number of distances to consider. If we consider the reduced eye, with a single principal plane, and nodal point. The principal plane is 1.5mm behind the anterior surface of the cornea, and a nodal point 7.2mm behind the anterior surface of the cornea. This gives an anterior focal length of 17.2mm measured from the single principal plane to the anterior focal point (F1), 15.7mm in front of the anterior surface of the cornea. The posterior focal length of 22.9mm is measured from the same plane to the posterior focal point (F2) on the retina. 

The problem with some calculations is that they fail to take into account the fluid-filled properties of the eye. Now calculate the Dioptric power of both focal lengths, using the refractive index of vitreous humour = 1.337 for the calculation of the posterior focal length :

diopter, anterior focal length = 1000/17.2 = 58.14
diopter, posterior focal length = (1000 * 1.337)/22.9 = 58.38

what about aperture?

What does this allow us to do? Calculate the aperture range of the human eye. If we assume the iris diameters are 2-8mm, and use both 17mm and 22.9mm we get the following aperture ranges:

17mm : f2.1 – f8.5
22.9mm : f2.9 – f11.5

Does any of this really matter? Only if we were making a comparison to the “normal” lens found on a camera – the 50mm. We’ll continue this in a future post.