does The speed of light in air depends on wavelength and light frequency
the speed of light doesn't depend on anything. It is constant.
The speed of light is the property of light. As well as its wavelength and frequency. It travels slower in air because there are particles in air, and therefore denser. This causes the light to travel at a slower speed.
uv light may be blocked by glass while even higher frequencies like x-rays and so on are blocked by led the index of refraction lists different mediums like water ,oil and other mterials are listed in hyperphysics vault that speak of such things as snells law, in short yes and gravity may also effect certain nm of light, nice question.
I think temp may effect light as well though I am not sure how temp would effect light in a vacume
Yes, the speed of light does depend on the wavelength through air. The air slows down the light, and how much depends on wavelength/frequency. This is the same reason different wavelengths of light are bent at different angles through water, glass, ect, and rainbows form.
The speed of light "in a vacuum" is taken to be a constant. Yes, you can slow light down by making it pass through stuff like air and glass and water. It is just a number, a constant, used in calculations. Frequency does not have an effect on the speed of light but it does effect wavelength as they are inversely proportional to each other.
And you will have seen in the news yesterday that some boffins at CERN think they have been zapping particles about just a tad faster than the speed of light - which will be very inconvenient indeed if it is true.
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