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If i am looking at an object which is moving towards me fast enough while i am at rest, then i would see the object's color shift towards blue in the Electromagnetic spectrum. But would the same happen(will it look blueish) if i am moving towards the object while the object is at rest.

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  • $\begingroup$ Reallyyyy fast yes. $\endgroup$ – Alchimista Mar 20 '18 at 17:33
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Yes. Light and other forms of electromagnetic radiation propagate through space without requiring a medium. Without that medium, the only information necessary to determine the frequency shift is the relative velocity between the sender and observer.

So sender moving to observer and observer moving to sender are identical situations, and the frequency shift is calculated using only the relative velocity of the two:

$$f' = f \left(1 + \frac vc \right)$$ ($v$ positive when motion is bringing the sender and observer together)

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