Red

Red is how we perceived the longest-wavelength (and thus lowest-energy) light that our eyes can detect. As wavelengths get shorter they look yellow, then green, then blue. Any hue not on this progression is caused by the combination of multiple wavelengths.

Objects can look a given color in two broad ways. Either they can take the incoming light and reflect it back in all directions equally, which we call diffuse lighting; of they can bounce photons off of them like a rubber ball off a wall, which we call specular lighting. Specular lighting can look like a mirror if the object’s surface is smooth, or if can look like a cloudy mirror or brushed or powder-finished metal if the surface is rough.

Eyes

An eye is a biological device for detecting how much light is arriving from each direction.

The retina is the part of the eye that detects light intensity, but it itself has no directional detection capabilities. It does know where on the retina light is and where it is not, but it can’t tell what direction the light came from to hit a given part of the retina.

The sclera surrounds most of the eye with the primary purpose of being opaque, keeping light from getting in to the eye (and hence reaching the retina) from most directions. It has one opening, called the pupil, with a ring of opaque muscle called the iris at this opening to allow the pupil’s size to be adjusted.

If the pupil were very very small, then any light that reaches a given point on the retina had to enter through that tiny pupil meaning it had to come from a specific direction. But almost no light would find a pupil that tiny so instead the pupil is larger with a lens inside it to focus light with the same goal as a tiny pupil: light coming into any part of the pupil from a given direction should all be bent to hit the same region of the retina.

There are also a few other parts of the eye: a transparent covering over the pupil and lens called a cornea and a transparent substance called vitreous humor inside the eye to help keep its shape, as well as a few others that are not visible when looking at the eye.

Transparency

There are two ways to be transparent: dielectric or metallic.

Dialectic materials (basically everything except metal) are mostly transparent with non-transparent particles inside. By transparent I mean that a photon encountering them slows down (and hence changes direction a little) but does not otherwise interact with the material. And then one of two things might happen.

In most materials, the photons inside the material almost immediately encounter something that interrupts their journey and are either absorbed or deflected in a random direction. After several such bounces they emerge again, usually quite close to where they entered, creating a diffuse lighting effect. The color of the emerging light is dependent on which wavelengths were not absorbed, which for most materials is mostly the shorter more-energetic wavelengths: low-energy photons can only be absorbed by something that has an energy state quite close to its current state while high-energy photons can often jump several energy states. This is why there are very few things in the world that are not some color that reflects more long-wavelength than short-wavelength light (i.e. red, orange, yellow, brown, or gray) except for chlorophyll (which has a biological imperative to interact with light in one specific way and hence is a little picky in what wavelengths it can absorb) and pigments created by living things to attract the attention of other living things (like flowers and feathers and ink, though even those are more often on the long-wavelength-color spectrum).

In a few materials (notably air and water) there are so few photon-interacting particles inside the transparent medium that light can travel a long way through it. However, even if fully pure there’s a small chance that some molecule much smaller than the photons themselves will still deflect the photons in a random direction, with the likelihood of that increasing the closer the photon and the molecule are in size. This always means that more blue light gets scattered than red light, meaning that light that makes it through scattered tints yellow (or even red if the fluid is very thick) while the medium itself look blue (a rich dark blue if it’s thin, moving towards cyan if it’s thicker).

In addition to dialectic transparency, very thin films of some metals (a few nanometers thick) have some photons travel through them unimpeded by the metal. The amount of light that makes it through depends on the metal used, but also on its thickness in less-than-intuitive ways; I don’t fully understand this process¹¹ and it seems to be an area of ongoing research; see, for example, https://doi.org/10.1016/j.phpro.2012.03.510 but it does require unbroken sheets of metal many times thinner than a cell wall.

Thin films of transparent dielectric material can have an oil-slick-like diffraction effect that results in an angle-dependent rainbow of colors.

Colored pupils

The ideal way to have a red pupil would be to diffuse red light outward but have all light transmit inward. However, I know of no way to achieve that. A blue pupil could conceptually be created by making a very optically-dense air-like substance (maybe like an aerogel but optically thicker), but that won’t work for red.

A nanometer-thick copper film over the pupil would give it a copper-like appearance, which is as red as I know how to get with transparent metals. But no biological process on Earth creates anything like that, and it probably wouldn’t be called red pupils if it did exist.

Red sunglasses exist, but they work by absorbing most non-red light. Merge them with the eye and the pupil (which absorbs all light) would still look black.

A translucent red material (effectively a cloudy lens and a red sunglasses combined) would look red and would allow some light into the eye. However, much of that light would be diffused, making the lens ineffective. If it was only slightly cloudy there might be enough direct light to see something while still looking like dark reddish-brown pupils, but diffused light would overwhelm and mask dark shades²² Similar to how white noise overwhelms and masks quiet sounds making the eyes much less effective.

And that’s the best I’ve got. Red pupils can be created, but only by either

1. Appealing to magic or undiscovered science to postulate a red-scattering material or red-appearing metal film; or

2. Having the creature invest biological effort to be half-blind.