What really determins the color of light? I have been considering this problem:

Colour is characterized by which of following character of light?
a)Frequency
b)Amplitude
c)Wavelength
d)Velocity

Different websites claim different answers; some claim wavelength, some claim frequency. My textbook is an average Indian textbook and has wavelength as the answer. I searched in standard books but did not find the answer.
But, as the wavelength changes from one medium to another medium, frequency does not change, and colour also does not change, it seems confusing to decide between frequency and wavelength. I consulted a teacher as well, he said wavelength, with logic I did not understand, and as he seemed to be in a hurry I did not feel comfortable to prolong the conversation.
References:
https://doubtnut.com/question-answer-physics/the-colour-are-characterized-by-which-of-following-character-of-light--14159721        // says frequency
https://doubtnut.com/question-answer-physics/statement-1-the-colour-of-light-depends-on-its-wavelength-and-statement-2-on-passing-through-from-on-69130668           //says wavelength but answer mentioned(in the lower section of webpage) is frequency.
https://www.toppr.com/ask/question/the-colour-are-characterised-by-which-of-following-character-of-light/   //says wavelength
https://brainly.in/question/11025304             //says wavelength 
What determines color -- wavelength or frequency?  //says frequency
 A: Other answers are saying it's frequency alone. That is not true. Frequency does, however, play the biggest role in perception of color. Especially when neglecting edge cases like humans hardly perceiving any color in low-light conditions due to cones being less light-sensitive than rods. Rods only support monochrome vision (brightness only; no color). Furthermore, because rods tend to be on the outer edges whereas cones are in the center of your field of vision, you don't really perceive color at the edges of your field of vision. Your brain remembers the color objects there should be.
But the biggest flaw I see in this focus on frequency is relative color. You can try this yourself. Find the brownest brown you can find and fill your entire screen with it. Then turn all the lights in your room off and make sure no light enters through the windows. Your only source of light should be your entirely brown monitor. But it will not be brown. It will be orange. Brown is just what we call some shades of orange when there is something brighter around. But as in this setting brown is the brightest thing, there is no brown. Only orange. Yet no one would argue that brown and orange are the same color. Therefore, color does not only depend on frequency.
If you don't want to find your own brown and trust me and the first result on Google Images, I've prepared some nice brown for you:

Right-click the image, click "View image", press F11 to switch to full screen, and zoom in by scrolling up while holding Ctrl down. Your screen should be completely brown. I mean orange.
Oh, and remember when I just told you that no one would argue that brown and orange are the same color? That's not true. The set of colors people see is changing. In the past, orange wasn't its own color. Most shades of orange belonged to red. Or take pink. This image is labeled in German:

You'd call both of them "pink" in English. Cultural context matters. Not only temporal context, relative brightness, position in your field of view, and of course, frequency. Color is about more than just properties of light, and even when only focusing on properties of light, it's not just frequency. And thereby also about wavelength. Because wavelength is just the multiplicative inverse of the frequency of light (multiplied with the speed of light but that's a constant). 
A: You're right to be confused, light is a special case because its speed (in a vacuum) is always the same value. In the equation
$$\nu=\frac{c}{\lambda}, \tag{1}$$
$c$ is a constant. This means that for light (not for general waves), as soon as you know the frequency you immediately know the wavelength, and viceversa.
"Colour" on the other hand is a little harder to define, since people are capable of perceiving different wavelength of light as different subjective "colours".
A: 
Wavelength or Frequency

Wavelength ($\lambda$) and frequency $f$ are related by the speed of light ( $c$ ) :
$$\lambda = \frac c f$$
So either gives exactly the same amount of information.
I'll use wavelength for the remainder of the answer to be consistent.

Velocity

The speed of light in vacuum has no effect on color.  It's a constant.
The speed of light in different mediums (e.g air, water) is slightly different from than in vacuum and has a dependency on wavelength.  This doesn't really have much effect on color (which is a human perception) but is the reason why you can use e.g. a prism to split white light into different wavelengths.  Different wavelengths are deflected ( refraction ) by different amounts and this effectively splits the light for you.

Amplitude

Has no relevance to color.

Color

Color is a human perception based on how we sense light.  We have three different receptors in the eye that respond slightly differently to different wavelengths.  This lets our brains differentiate the different wavelengths better.
If we had just one receptor type we'd only see in black and white (levels of grey).
If we had two we'd have a more limited ability to tell different wavelengths apart and we'd get a lot of them confused.
Three (as worked out by evolution) is an optimal system for use - just complex enough, but not too complex.
However because of the way we interpret light, mixed wavelength light produces a mixed color.  That's what we can see e.g. brown - there is no single wavelength corresponding to brown, it's result of how our brains detect multiple wavelengths at the same time.
This is also why we use RGB as the basis for so much of our color technologies.  We need three components to describe a color.  Most other color systems use three components except for some specialist ones for specific purposes.
Wikipedia's page on Color Vision goes into more detail and links to even more detail if you need more information.
A: There is this similar question on a sister site which is well answered IMO. Actually

It is not the wavelength or frequency that determines light absorption- it is the energy of the photon that matters. The energy of incident light should match the excitation energy of the chromophore. The medium itself can also affect light absorption by electronically interacting with the chromophore. Frequency is proportional to the energy (given by the relationship $E=h\nu$); while wavelength and velocity change in different media, frequency and energy remain constant.

So in other words, the frequency is the key factor. But the overall light flux is also important to activate enough retinal cells to transmit the color signals.
A: The answer is energy. Now for photons, E=h*f, so this will give you the answer as frequency. Frequency is proportional to energy.
Now you are confused, because most people would say wavelength. It is true, for vacuum, where frequency and wavelength could both be proportional to energy.
But in a medium, frequency is the only one that is proportional to energy, and that is the answer.
A: Frequency. As you mentioned, wavelength changes in different mediums, but frequency doesn’t. If you look at a red ball underwater, it still looks red, even though the wavelength of the light is quite different.
A: The equation of velocity of light is 
$v=f λ$. If the source of light (frequency) is same then color of light depends on its velocity & wavelength.
In optics color depends on bending of light e.g dispersion of light.
