If our sun were not a small yellow star and was a different color, would rainbows still look the same?

No. The colors of the our rainbows occur because white light is in effect. Different sunlight colors would produce different colored rainbows. A red sun might have a rainbow that didn’t have red, or yellow, or purple. A blue sun might not have blue, or yellow, or the same green, or purple. Different colors would occur if our sun was actually yellow.

Size and class of star will not change the rainbow.

A star of any color radiates the entire spectrum of visible light. We have no problem resolving any of those colors from light emitted by our yellow sun. The physics of refraction hold in a prism or raindrop should regardless of the star’s apparent color.

The light refracted by a raindrop is entirely dependent on the light source, that is the sun. If the sun’s light changes colour the light refracted by the raindrop is going to change also. It might not be very noticeable but the proportions of the different colours in the rainbow will change.

The sun is not yellow. It just appears that way, because it is filtered through Earth’s atmosphere.
It is actually white.

Remember, White Stars Matter.

Especially when it comes to refraction of light. If the light source is no longer white/yellow, then the colors in the rainbow will refract differently.

Wait a minute fellas. Stars do of course come in colors and ours is yellow compared to the others. Those apparent colors are in fact more indicators of the temperatures of those stars just as with heated steel. Blue/white being hottest and red at the cooler end. And again, the full spectrum of light is there for refraction.

There would definitely be a shift in the spectrum from stars of different colors. It may only be slight.

Our sun is more green than yellow, but the best description (other than a chart of the actual spectral emissions) is probably white, when seen from space. When seen through the atmosphere of our planet, of course, it can seem to be different colors, such as yellows and/or reds or oranges.

Rainbows are products of atmospheric refraction, where the white light gets spread into different colors in different directions by frequency.

A different star would have slightly different frequencies, and a different atmosphere would filter and refract slightly differently… but a rainbow effect would still be essentially the same, because it is how our eyes perceive the spectrum of light, and other stars would still contain more or less the full spectrum, if in somewhat different arrangements.

Here is an example of a lens flare (not a rainbow, but still) on Mars: https://twitter.com/NASAPersevere/status/1379536046338154498

Do our eyes have any impact on how things would change or not? Our eyes can only see a certain range of electromagnetic wave lengths. So if the color of the sun were different, would we really see any change?

Of all our senses, none compare to the importance of sight in our brain’s adaptation to interpreting the world From the extraordinary amount of brain area devoted to vision to the fact that our eyes are literally physical components and outgrowth of the brain itself. So of course our eyes are suited to refract certain frequencies. Clearly there are creatures designed to refract (“see”) colors we miss, and it’s daunting to understand that there are uncountable numbers of colors between yellow and orange, and to appreciate that there is no way to determine when 2 of us “see” the same object, our brains interpret them identically. Is your yellow actually a shade of my green?

It’s not a hypothetical question as astronomers can analyse the spectra of individual stars. While stars emit light over the entire electromagnetic spectrum not all stars emit the same amount of energy at all wavelengths. Each star has a peak emission of thermal radiation that depends on its temperature. Hot stars (or suns) emit mostly blue light and the red part of the spectrum is dark. Cooler suns emit mostly red light and the blue part of the spectrum is dark. So yes, we would see a difference.

@seawulf575 Yes, our eyes are sensitive to certain frequency ranges (which vary by individual) and our brains interpret the colors, giving us our perceptions.

So we will see changes in light, but only in those frequencies, whether the changes are due to the different sun’s light (which mostly wouldn’t be very different except in size – there would still be a lot of light throughout our visual range, so it would mainly be white), or due to the local atmosphere (which unless it were close to Earth’s, I expect would tend to cause more difference than the sun).

Scientists can ID a star by it’s spectral shift.
“spectrum… 1. Physics. The series of images formed when a beam of radiant energy is subjected to dispersion and then brought into focus, so that the component waves are arranged in the order of their wave lengths; hence, any series of radiant energies arranged in order of wave length. The “visible spectrum” has wave lengths between 3,800 and 8,000 angstrom units and when of sufficient intensity evokes in the eye a series of colors ranging from red (evoked by waves of 760 millimicrons in length) to violet (385 millimicrons).” -from Webster’s New Collegiate Dictionary, 1960 ed.