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The phenomenon of 'blue shift' occurs when a light source moves closer to an observer. In this case, the wavelength of light decreases, causing the light to appear 'bluer' than when it is at rest or moving away. This happens with any electromagnetic wave, including visible light. For instance, in the context of galaxies, a blue-shift would imply that the galaxy is moving towards Earth. The reason it's called a 'blue shift' is that in the visible spectrum of light, blue has a shorter wavelength compared to other colors, and a shift towards shorter wavelengths leads to a shift towards the blue end of the spectrum.

This is an essential concept in astrophysics as it helps determine the relative motion of celestial bodies. If scientists find that the light from a distant galaxy is blue-shifted, like in the case of the Andromeda galaxy, it tells them that the galaxy is approaching us.

The calculation of the Doppler effect for light involves measuring the change in frequency or wavelength of the light due to the relative motion between the light source and the observer. The standard formula for Doppler effect calculation in the context of light is: \[\begin{equation}\frac{v}{c} = \frac{\Delta f}{f}\end{equation}\]where 'v' represents relative velocity, 'c' is the speed of light in vacuum, '\Delta f' is the frequency change, and 'f' is the original frequency. By manipulating this equation, one can solve for the relative velocity, which will indicate how fast the source is moving towards or away from the observer.

Relative velocity is a measure of how fast one object is moving in relation to another. In the context of Doppler effect and astronomical observations, relative velocity refers to the speed at which a celestial object, such as a galaxy, is moving towards or away from Earth. It's essential since it helps astronomers determine the dynamics of our universe, including expansion and the motion of galaxies. Calculating this velocity can reveal not only the motion of the galaxies but also provide clues about the underlying structure and history of the cosmos.

Frequency change is the difference between the observed frequency of light and the frequency at which it was emitted. This shift occurs due to the Doppler effect when there is relative motion between the source and the observer. If the source is moving closer, the frequency increases, corresponding to a blue shift. Conversely, if the source is moving away, the frequency decreases, leading to a red shift. Frequency change is directly proportional to velocity; however, because the speed of light is so great, changes in frequency for most celestial objects are small and require precise instruments to measure.

The speed of light in a vacuum, denoted by the symbol 'c', is a fundamental constant of nature and is approximately 299,792,458 meters per second, or about 300,000 kilometers per second. It's not just the speed at which light travels; it's also the speed at which all electromagnetic radiation propagates in a vacuum, such as radio waves, X-rays, and gamma rays. The invariable speed of light is vital in the Doppler effect calculation for light because it is the constant with which all frequency changes, as observed in a vacuum, are compared.