# Minimal and Maximal Exit Pupil | Optics Trade Debates

Hello everyone and welcome to another Optics Trade Debates video. Today, we’ll be discussing the terms minimal and maximal exit pupil.

Let’s start with a simple definition. The exit pupil is the diameter of the light that exits through the optical instrument. If the optical instrument provides a singular, fixed power of magnification, the exit pupil diameter too is constant in value.

The exit pupil diameter can be calculated with the simple math formula of dividing the lens diameter specification with the power of the magnification. For example, a rifle scope or a pair of binoculars with the specifications of 50-millimeter objective lens and 10x magnification will have the exit pupil of 5 millimeters.

While the diameter of lens is a fixed measure, the variable magnification means that there are minimal and maximal exit pupil values. With a 2-10x50 rifle scope, where the power of magnification setting can be adjusted anywhere from 2 to 10, the smallest exit pupil is set at 5 millimeters and the biggest one possible at 25.

We conducted a simple experiment to show how minimal and maximal exit pupils work in practice. The instrument used in the video is a Swarovski Z8i 0.75-6x20 rifle scope. Using a flashlight, we direct a beam of light into the instrument lens and observe the size of the circle against the white box. This circle, specifically its diameter, represents the exit pupil.

When the magnification power is adjusted to 6, the edge of the exit pupil is completely shut and provides for the proper eye relief. Knowing that the lens diameter is 20 millimeters and dividing it by the magnification power of 6, tells us that the exit pupil is now set roughly at 3.33 and the visual in practice matches our calculation. If we reduce the power of magnification, the circle exponentially grows and with that the exit pupil diameter. Inversely, at its maximum, the exit pupil should be roughly 20 mm in the diameter since the 20 mm lens divided by the magnification of 1 is 20.

This is a good visual presentation what the maximal and minimal exit pupil factors mean in practice. The exit pupil is at the maximum when the instrument is used with the minimal magnification power available, and at its minimum when the instrument settings are adjusted to its maximal magnification power.

However, note that the human eye can only dilate to 8 millimeters and cannot make use of excessive light that filters through the optical instrument beyond this range. This is why all premium scopes, including the Swarovski Z8i 0.75-6x20 used, limit their maximum exit pupil to around 10 millimeters.

Although we used a rifle scope in the video, this method of calculation is practically universal and can be also employed with other optical instruments such as binoculars, spotting scopes and all classical which have a variable magnification.

It is also important to mention that there might be some deviations in how much the human eye can dilate. In theory, the pupil diameter in the human eye changes in different lighting conditions from 3 to 8 millimeters. But in practice there are other factors, such as the individual’s advanced age and health issues, that can affect the eyes’ ability to dilate.

The standard optical instrument will already provide an exit pupil diameter above 10 millimeters, beyond the needs of the human eye that cannot use all the excess light that filters through. Still, individuals with a bigger eye exit pupil can enjoy a more forgiving eye box since their eyes can comfortably move anywhere within the circle diameter space and will still receive a clear image.

Explanation of the term on our website:

#### Max. exit pupil diameter

Maximal exit pupil diameter is an important information when you are buying an optical product, that will be in use in the twilight. This information tells us, at what diameter the light comes through the optical product, where it then enters the pupil in the human eyes.
The exit pupil diameter can be easily calculated from the magnification and objective diameter of the optical product. The objective lens diameter has to be divided by magnification, and then you get the exit pupil diameter.
For example; an 8x56 binoculars have an exit pupil diameter of 7 millimeters, and 10x42 binoculars have an exit pupil diameter of 4.2 millimeters (56:8=7; 42:10=4,2).
The pupil diameter in the human eye changes in different lighting conditions from 3 to 8 millimeters. On a bright sunny day, the pupil is very small, because of the excess light. In the twilight, the pupil gets bigger so more light can pass through to the retina.
So if you have a 10x42 binocular, which has a 4.2-millimeter big exit pupil diameter, you won't have as a bright picture like with the 8x56 binocular. This is because the pupil of the human eye will be at its maximum dimension of 8 millimeters, but the light will come through the binoculars only in 4.2 millimeters.

It is a little bit different with variable magnification optical products. There the exit pupil diameter isn't always the same dimension, but it changes simultaneously with the magnification. For example; if we have a rifle scope with a magnification of 3-12 and an objective diameter of 56 millimeters, at maximum magnification we have an exit pupil diameter of 4,7 millimeters. At the smallest magnification on the other side, the exit pupil diameter should be 18.7 millimeters, but because such a big diameter would not have any advantage (because the human eye pupil is maximal 8 millimeters big), the manufacturers install an optical insert which doesn't let the exit pupil diameter grow too big at small magnifications. This is also our maximum exit pupil diameter. If we take the magnification of 7 times, the exit pupil diameter is 8 millimeters, what would be perfect for the brightest picture through this particular rifle scope. 