When an electromagnetic field passes through different mediums, it is known that it will refract. And during refraction – since its frequency is kept constant – the only parameter that changes is its wavelength which intern will change its speed. With this keeping in mind lets look at this prism that disperses light.
When the white light comes to the prism it has a speed of $c$. But after it is refracted by the prism, hadn't its speed change? And if that happens, wouldn't it contradict with the fact that all electromagnetic waves have the same speed?
The second question is, could two electromagnetic waves of different speed and wavelength have similar color?
The following is my reason for this question. It is thought that light is composed of the other seven colors (by the way what does composed of mean in this sense?) Right? During the dispersion by a prism, each component will refract by different angles, having new wave lengths and new speeds, which means they had a different wave length and speed before refraction. Which intern means the red we see after refraction isn't the red that made up the white light unless electromagnetic waves of different wavelength and speed can be perceived as similar by the eye?
Best Answer
In vauum, all the electromagnetic waves have the same speed $c$. When the wave passes through a material, such as the glass of a prism, the speed is decreased, but only during the passage, inside the material. When the wave exits from the prism, its speed comes back to the speed $c$ (or slightly less, if the wave is propagating in air instead of vacuum).
When the wave enters into the prism, it keeps its frequency (how many periods per second). But, since it is slowed down, its wave length becomes shorter: in a period, it travels a shorter path. But, also in this case, when the wave exits, it takes back its wave length, the same it had when it entered.
Coming to the second question. It is useful to think that the color of the light is associated to the frequency, which never changes in refraction, reflection and diffraction processes. Frequency is important because the "sensors" in our eye are sensitive to the photon energy, which depends on the frequency. On the other hand, the speed of light in our eye depends on the material of the eye itself, so there is also a well defined and fixed relation between wave length and frequency!
So said, a beam with a given color, after passing through a glass prism or a lens, will still have the same color. Of course, its wave length will change along its path, but our eye will never know it.
Finally, what does it mean that a beam is the superposition of various wave lengths? This would deserve a separate question, but this can help to understand the principles:
https://demonstrations.wolfram.com/SuperpositionOfWaves/