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Exit pupil

Exit pupil is the diameter of the beam of light exiting the eyepiece.

The exit pupil can be calculated in several ways:


$$ \small \begin{align} d &= \text{exit pupil (mm)} \newline D &= \text{Aparture (mm)} \newline P &= \text{Power (magnification)} \newline \end{align} $$

$$ \large d=\frac DP $$


$$ \small \begin{align} d&= \text{exit pupil (mm)} \newline D&= \text{Aparture (mm)} \newline f&= \text{eyepiece focal length (mm)} \newline F&= \text{OTA focal length (mm)} \newline \end{align} $$ $$ \large d=\frac {D\cdot f}{F} $$


$$ \small \begin{align} d&= \text{exit pupil (mm)} \newline f&= \text{eyepiece focal length (mm)} \newline R&= \text{focal ratio (e.g. f/5)} \newline \end{align} $$

$$ \large d=\frac {f}{R} $$


Using a too great of a magnification results in a very small exit pupil (sub 1 mm). This causes any small objects in the light path to become visible, from small dust particles on the eye lens to the floaters within the eye itself. This can become distracting when, for example, viewing the surface of the moon.

The second issue caused by a small exit pupil is that it may be difficult for a novise to align their eye with the exit pupil. The position where anything is visible is very small. Since the exit pupil itself is small, when hitting the edge of the pupil, the view can disapear in an instant, instead of fading away gracefully, which is how a larger exit pupil would behave.

The issue is exasperated by viewing a bright object. This causes the eye pupil to contract, making aligning the small pupil with an even smaller exit pupil very difficult.

$$ \large 0.8\ mm=\frac {80\ mm} {100x} = \frac {80\ mm \cdot 5\ mm} {500\ mm} $$

If, on the other hand, a too low of a magnification is used, the exit pupil may be larger than the pupil of the viewer. This causes some of the light to miss the pupil, reducing the effective brightness and wasting part of the telescope aparture.

Human maximum pupil size is approximately 7 mm, but gradually decreases with age.

$$ \large 9.5\ mm=\frac {200\ mm} {21x} = \frac {200\ mm \ \cdot 32\ mm}{675\ mm} $$

A large or even over large exit pupil is easier to use, since aligning the eye is very easy and reaching the edge of the exit pupil would cause a gradual fade, instead of blinking out.

Telescopes with large apartures are typically of the Newtonian or Cassegrain types, meaning they have a secondary mirror obstuction. The obstruction is preasent even in the exit pupil. If the exit pupil is larger than the physical pupil, it’s possible that the central obstruction may cause the image to get dim or even disapear, while viewed perfectly centered. This may make viewing once again difficult.

Depending on the eyepiece, this may also result in kidney beaning - a phenomenon where dark areas in the shape of kedney beans may appear and obscure part of the field of view.