Question

why can we only see the domain of the visible in the electromagnetic spectrum?

Answer 1

The short answer is because we evolved to have sensors that only detect that range of EM radiation.

Now the question becomes why that part of the spectrum? One reason is that it is the strongest part of the spectrum in the precise sense that it represents an interval of the EM spectrum which the sum emits the most of. See the diagram below:

Since humans evolved to do the majority of our important activities during the day, it makes sense that we take advantage of the most available reflect EM radiation available.

The eye has evolved around 40 times independently on earth and each time what we call the visible spectrum is part of the range of the vision for those eyes.

There is obviously some sort of trade off between range of spectrum we can perceive and our ability to perceive it. That is to say, arguably we could have evolved eyes that can perceive more of the spectrum. But keeping the eye the same size, that would mean we would detect less of it. Clearly over millions of years, it was found that this eye size with this range of spectrum with this ability to detect it was optimal.

Arguably therefore life that evolves on planets whose sun is hotter will have vision centered around higher frequency light, in the UV, X-ray or maybe even gamma ray range; and life that evolved on planets whose sun is cooler than ours would have vision centered in the infrared region.

Answer 2

(Our sun has a surface temperature of 6000 K which is why it has that blackbody radiation distribution. You can see the distributions for cooler black bodies marked on the graph as well.)

Answer 3

I would like to add something to what JamesJ rightly said: visible light reaches us because the Sun emits a lot in that area of the electromagnetic spectrum AND because the atmosphere is transparent for those wavelengths too.

Answer 4

Actually the sun is emitting the spectrum which consists of all the wavelenghts right from the radio waves to the cosmic rays. Our eye can SENSE only the visible portion of the electromagnetic spectrum. Hence we see only the visible radiations only.