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What is meant by the terms red-shift and blue-shift?

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Answer
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Hint :The redshift and blueshift is observed in the doppler shift. Doppler shift is also known as Doppler’s effect. Doppler’s effect can be defined as the change in the frequency of the wave with respect to an observer which is moving relative to the wave source.

Complete Step By Step Answer:
Red Shift
Red shift is the movement of spectral lines which is towards the longer wavelengths which is the red end of the spectrum in radiation from the distant galaxies and the celestial objects.
A red shift is any increase in wavelength with the corresponding decrease in the frequency of an electromagnetic wave.
The value of the redshift is denoted by letter z and is corresponding to the change in the wavelength which is positive.
Blue Shift
Blue shift is the movement of spectral lines which is towards the shorter wavelengths and is the blue end of the spectrum in radiation from the distant galaxies and the celestial objects.
With the corresponding increase in the frequency of an electromagnetic wave, the blue shift decreases its wavelength.
The corresponding change in the wavelength is negative for the value of the blue shift.

Note :
Similar effect is observed when the galaxy moves away its light is more stretched and it moves to the red end of the spectrum which is known as the redshift. Similarly when the galaxy moves towards us its light is compressed and becomes bluer which is known as blueshift.