Yes, it’s normal. I have similar experiences with my eyes. If I recall correctly, blue eyes actually lack pigment (melanin) that would otherwise give them color on their own. Light bounces off the unpigmented iris and scatters… And the eye winds up looking blue for I believe a similar reason the sky looks blue. The environment can affect, to a certain extent, what light hits the iris—meaning that, to a certain extent, the eye can seem like it changes color. My own eyes can seem to range from dull gray to blue to teal (I have a small amount of yellow on the inside of my eyes, I think that helps with the teal effect)... And I know this for a similar reason you do, that people have told me.
If I also recall correctly, there are two layers of pigment to the iris. The back player’s reflected light has to pass through the front layer, and somehow that makes it appear yellow… These dual layers and the amount of pigment on either of them give us the wide range of eye colors we see. (If I also recall correctly, green eyes are a combination of pigmented back layer, and of unpigmented front layer—so yellow plus blue).
—I’m trying to remember the source I got that information from. I’ll link it when I remember and find it
again.—
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