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It depends on how the eye is build exactly.

Horses have some of the largest eyes of land animals with up to 5cm in size (some squids have soccerball sized eyes but they have different light exposure). So size isnt the issue.

Hawks have similar size eyeballs as humans, but way larger pupils (https://images.app.goo.gl/xf8cQcrU7QECDGgt8). So overexposure isnt an immediate problem. However a larger pupil means you need a deeper eye for a sharp picture.

Aye ayes and other nocturnal creatures also use large eyes for their size in order to gather more light. Often complemented with a kind of mirror behind the fotosensitive cells to reflect the light and catch more with the cells. This is the reason why shining in the eyes of for example cats and dogs their eyes light up so weirdly.

If you go for nocturnal eyes the size can help them to see but not necessarily help them see sharply. If you go for sharp or hawk vision you have another problem: eyeball size. With eyes that big the rest of the organs in the head will have less space. This will limit the nose cavity and breathing, which will have to be moved lower in the head. This means that your mouth will be smaller and eating will be harder or your face needs to be longer. But that is nothing when you consider the brain. If you keep human dimensions their brain will be smaller, and their intelligence will suffer for it.

I'm no biologist so I'll stay away from skull size, capturing more light or others physiological effects that L.Dutch and JBH already covered; instead I will focus on a more psychological aspect.

Big eyes convey a lot of non-verbal communication

Big eyes in animation are a trope because "eyes are the mirror of the soul". This is the part of the body most of us notice first. Also, eyes are capable of conveying a lot of information for someone who can read it: envy, lies, fatigue, sadness... human have evolved to a point where we can understand other's emotions without having even beginning to talk.

My guess is that bigger, anime-style eyes, would be much more mobile and expressive. The average human eye has twelve muscles, and i'm not counting those for the eyelashes, etc. With eyes twice the size, these muscles could provide a lot more of expressions, from the most subtle wink to a full black-eyed pupil.

So, what's the use?

Seduction/intimidation

Big eyes convey empathy. When you crave for something, be it a sexual partner or that fancy pair of shoes, your subconcious make your eyes widen, so you can capture more light and see better what caused this sudden urge. And, on the other side, it is known that dilated pupils are considered as more desirable traits when seeking for a mating partner.

But your eyes also widen more when in conflict. This is one of the answers of our body for an imminent fight-or-flee situation: we are aware there is danger and we are already seeking an exit. Showing big eyes with black dilated pupils at this point is telling your opponent: "I am ready to fight" and can be a factor of intimidation. This is why some animals sometimes show "fake eyes", they serve as a way to fool predators into thinking they are staring at the face of an even bigger creature.

Long story short: your big-eyed humans may probably demonstrate more animal behavior, related to instinct, when it comes to seduction or intimidation, and may be able to read other people's emotions much more accurately, to the point it could even look like a form of telepathy.

Can eyes be something other than spherical?

I don't have the anthropological expertise to know if there are any eyeballs in nature that aren't spherical. If nature can only make a spherical eyeball, then one of the consequences of a larger eye is less space for either (or both) the brain or the sinuses. It might also impact hearing as larger eyes might impact the auditory channels (although I believe this has a low chance of happening, unless the eyes are huge).

The result is a drop in breathing efficiency and mental capacity.

It also would require a wider skull (which might offset the two items I just mentioned). The closer together the eyes, the less valuable our 3D vision. Our brains use the data from the two eyes to "triangulate" objects in 3D space. Bigger eyes would mean wider spacing which would improve 3D acuity. And it would make our faces look much flatter. It would also increase the "blind spot" between our eyes as something approaches our noses (or, more specifically, the bridge of our nose). That would lower our ability to react to objects that might damage our eyesight or heads.

Pros:

• Better 3D acuity

Cons:

• Less space for the brain (less brain = bad)


• Less space for sinuses (harder to breathe and filter the atmosphere)


• Increases vulnerability.

But, what if they could be elliptical?

We can recover a lot of that lost space for the brain, etc, if we allow for elliptical and flattened eyes. But that has a terrible cost. Without the sphere, the "mathematics" of processing light become much more complex: and biologically that would most likely result in limitations. You also couldn't easily move the eyes with muscles, limiting the angular sweep the eyes can accommodate. So, you get the same pro, but pretty much the same number of cons, just different cons.

There was a human species with big eyes - the Neanderthals: see https://royalsocietypublishing.org/doi/full/10.1098/rspb.2013.0168

The effects may have been:

• can see in darker areas


• a larger part of the brain is used to process visual information


• which seems to have reduced the part dedicated to social interactions
  
  
  
  
  • so they were only comfortable in smaller groups
  
  
  
  


• and they are now extinct for some reason

Apart from the apparent size, i'd like to also take into account the (lack of) apparent curvature. The cleanest approach to explaining the movement, curvature and size while staying within the eyes current among Vertebrata would be to suppose giant spherical eyes many times the radius of the head. As they would overlap both themselves and the space outside the head, this might seem far fetched, but i'll still run with it (They also might be one big eye presenting with two pupils out of two openings, but the frequently observed crossing of the eyes invalidates that solution).

Bigger eyes mean higher possible resolution (as we can cram more retinal cells in there; and higher light capture, so better possible night vision. If we let the receptor cells get bigger too (sacrificing our gain in spatial resolution) we'll be able to catch light of longer wavelength (NIR) more efficiently (This is not heat vision (unless you mean near-glowing-hot-heat vision)!). Higher radius also comes with higher rotational inertia, and even if the eye's muscles scale too, there will be loss in acceleration (all effects up to now dealt in area-dependent effects, and muscle force also scales as the area, thus the available moment scales as r cubed, while moment of inertia scales to the fifth power of r ), this loss will be severe - we can posit the absence of saccades in anime.

If we wanted to get all the flexibility of anime eyes in the real world, we'd have to make them flat and squishy, with a display-like ability to change color, at least between black and white, and some muscles to change their size, aspect ratio and curvature. This would obviously mean compound eyes, where interferometry and the ability to focus a lot of the compounds in any direction (even relative to the changing eye geometry) could be used to even out the disadvantages (nearsightedness) insects have to deal with.

The change of color could be a sunglass like function - with white reflecting more light, and black letting more light in.